christopher/oeis · Datasets at Hugging Face

a-number stringlengths 7 7	sequence sequencelengths 1 377	description stringlengths 3 852
A000201	[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "33", "35", "37", "38", "40", "42", "43", "45", "46", "48", "50", "51", "53", "55", "56", "58", "59", "61", "63", "64", "66", "67", "69", "71", "72", "74", "76", "77", "79", "80", "82", "84", "85", "87", "88", "90", "92", "93", "95", "97", "98", "100", "101", "103", "105", "106", "108", "110" ]	Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.
A000202	[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "34", "35", "37", "38", "40", "42", "43", "45", "47", "48", "50", "51", "53", "55", "56", "58", "60", "61", "63", "64", "66", "68", "69", "71", "73", "74", "76", "77", "79", "81", "82", "84", "86", "87", "89", "90", "92", "94", "95", "97", "99", "100", "102", "103", "105", "107", "108", "110" ]	a(8i+j) = 13i + a(j), where 1<=j<=8.
A000203	[ "1", "3", "4", "7", "6", "12", "8", "15", "13", "18", "12", "28", "14", "24", "24", "31", "18", "39", "20", "42", "32", "36", "24", "60", "31", "42", "40", "56", "30", "72", "32", "63", "48", "54", "48", "91", "38", "60", "56", "90", "42", "96", "44", "84", "78", "72", "48", "124", "57", "93", "72", "98", "54", "120", "72", "120", "80", "90", "60", "168", "62", "96", "104", "127", "84", "144", "68", "126", "96", "144" ]	a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).
A000204	[ "1", "3", "4", "7", "11", "18", "29", "47", "76", "123", "199", "322", "521", "843", "1364", "2207", "3571", "5778", "9349", "15127", "24476", "39603", "64079", "103682", "167761", "271443", "439204", "710647", "1149851", "1860498", "3010349", "4870847", "7881196", "12752043", "20633239", "33385282", "54018521", "87403803", "141422324" ]	Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.
A000205	[ "1", "1", "3", "4", "8", "14", "25", "45", "82", "151", "282", "531", "1003", "1907", "3645", "6993", "13456", "25978", "50248", "97446", "189291", "368338", "717804", "1400699", "2736534", "5352182", "10478044", "20531668", "40264582", "79022464", "155196838", "304997408", "599752463", "1180027022", "2322950591", "4575114295" ]	Number of positive integers <= 2^n of form x^2 + 3 y^2.
A000206	[ "1", "1", "3", "4", "12", "22", "71", "181", "618", "1957", "6966", "24367", "89010", "324766", "1204815", "4482400", "16802826", "63195016", "238711285", "904338163", "3436380192", "13089961012", "49979421837", "191221556269", "733014218506", "2814758323498", "10825986453978", "41700030726757", "160842946895004" ]	Even sequences with period 2n.
A000207	[ "1", "1", "1", "3", "4", "12", "27", "82", "228", "733", "2282", "7528", "24834", "83898", "285357", "983244", "3412420", "11944614", "42080170", "149197152", "531883768", "1905930975", "6861221666", "24806004996", "90036148954", "327989004892", "1198854697588", "4395801203290", "16165198379984", "59609171366326", "220373278174641" ]	Number of inequivalent ways of dissecting a regular (n+2)-gon into n triangles by n-1 non-intersecting diagonals under rotations and reflections; also the number of planar 2-trees.
A000208	[ "1", "1", "3", "4", "12", "28", "94", "298", "1044", "3658", "13164", "47710", "174948", "645436", "2397342", "8948416", "33556500", "126324496", "477225962", "1808414182", "6871973952", "26178873448", "99955697946", "382438918234", "1466015854100", "5629499869780" ]	Number of even sequences with period 2n.
A000209	[ "0", "2", "-2", "0", "1", "-3", "0", "1", "-7", "0", "1", "-226", "-1", "0", "7", "-1", "0", "3", "-1", "0", "2", "-2", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-75", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-45", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-32", "-1", "0", "9", "-1" ]	Nearest integer to tan n.
A000210	[ "1", "3", "5", "6", "8", "10", "12", "13", "15", "17", "18", "20", "22", "24", "25", "27", "29", "30", "32", "34", "36", "37", "39", "41", "42", "44", "46", "48", "49", "51", "53", "54", "56", "58", "60", "61", "63", "65", "67", "68", "70", "72", "73", "75", "77", "79", "80", "82", "84", "85", "87", "89", "91", "92", "94", "96", "97", "99", "101", "103", "104", "106", "108", "109", "111", "113", "115", "116" ]	A Beatty sequence: floor(n*(e-1)).
A000211	[ "4", "3", "5", "6", "9", "13", "20", "31", "49", "78", "125", "201", "324", "523", "845", "1366", "2209", "3573", "5780", "9351", "15129", "24478", "39605", "64081", "103684", "167763", "271445", "439206", "710649", "1149853", "1860500", "3010351", "4870849", "7881198" ]	a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.
A000212	[ "0", "0", "1", "3", "5", "8", "12", "16", "21", "27", "33", "40", "48", "56", "65", "75", "85", "96", "108", "120", "133", "147", "161", "176", "192", "208", "225", "243", "261", "280", "300", "320", "341", "363", "385", "408", "432", "456", "481", "507", "533", "560", "588", "616", "645", "675", "705", "736", "768", "800", "833", "867", "901", "936" ]	a(n) = floor(n^2/3).
A000213	[ "1", "1", "1", "3", "5", "9", "17", "31", "57", "105", "193", "355", "653", "1201", "2209", "4063", "7473", "13745", "25281", "46499", "85525", "157305", "289329", "532159", "978793", "1800281", "3311233", "6090307", "11201821", "20603361", "37895489", "69700671", "128199521", "235795681", "433695873", "797691075", "1467182629" ]	Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.
A000214	[ "3", "5", "10", "32", "382", "15768919", "16224999167506438730294", "84575066435667906978109556031081616704183639810103015118" ]	Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).
A000215	[ "3", "5", "17", "257", "65537", "4294967297", "18446744073709551617", "340282366920938463463374607431768211457", "115792089237316195423570985008687907853269984665640564039457584007913129639937" ]	Fermat numbers: a(n) = 2^(2^n) + 1.
A000216	[ "2", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]	Take sum of squares of digits of previous term, starting with 2.
A000217	[ "0", "1", "3", "6", "10", "15", "21", "28", "36", "45", "55", "66", "78", "91", "105", "120", "136", "153", "171", "190", "210", "231", "253", "276", "300", "325", "351", "378", "406", "435", "465", "496", "528", "561", "595", "630", "666", "703", "741", "780", "820", "861", "903", "946", "990", "1035", "1081", "1128", "1176", "1225", "1275", "1326", "1378", "1431" ]	Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.
A000218	[ "3", "9", "81", "65", "61", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]	Take sum of squares of digits of previous term; start with 3.
A000219	[ "1", "1", "3", "6", "13", "24", "48", "86", "160", "282", "500", "859", "1479", "2485", "4167", "6879", "11297", "18334", "29601", "47330", "75278", "118794", "186475", "290783", "451194", "696033", "1068745", "1632658", "2483234", "3759612", "5668963", "8512309", "12733429", "18974973", "28175955", "41691046", "61484961", "90379784", "132441995", "193487501", "281846923" ]	Number of planar partitions (or plane partitions) of n.
A000220	[ "1", "0", "0", "0", "0", "0", "1", "1", "3", "6", "15", "29", "67", "139", "310", "667", "1480", "3244", "7241", "16104", "36192", "81435", "184452", "418870", "955860", "2187664", "5025990", "11580130", "26765230", "62027433", "144133676", "335731381", "783859852", "1834104934", "4300433063", "10102854473", "23778351222" ]	Number of asymmetric trees with n nodes (also called identity trees).
A000221	[ "5", "25", "29", "85", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145" ]	Take sum of squares of digits of previous term; start with 5.
A000222	[ "0", "0", "1", "3", "6", "38", "213", "1479", "11692", "104364", "1036809", "11344859", "135548466", "1755739218", "24504637741", "366596136399", "5852040379224", "99283915922264", "1783921946910417", "33840669046326579", "675849838112277598", "14174636583759324798" ]	Coefficients of ménage hit polynomials.
A000223	[ "3", "7", "10", "19", "32", "34", "37", "51", "81", "119", "122", "134", "157", "160", "161", "174", "221", "252", "254", "294", "305", "309", "364", "371", "405", "580", "682", "734", "756", "763", "776", "959", "1028", "1105", "1120", "1170", "1205", "1550", "1570", "1576", "1851", "1930", "2028", "2404", "2411", "2565", "2675", "2895", "2905", "2940", "3133", "3211", "3240", "3428" ]	Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where \|P(n)\| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).
A000224	[ "1", "2", "2", "2", "3", "4", "4", "3", "4", "6", "6", "4", "7", "8", "6", "4", "9", "8", "10", "6", "8", "12", "12", "6", "11", "14", "11", "8", "15", "12", "16", "7", "12", "18", "12", "8", "19", "20", "14", "9", "21", "16", "22", "12", "12", "24", "24", "8", "22", "22", "18", "14", "27", "22", "18", "12", "20", "30", "30", "12", "31", "32", "16", "12", "21", "24", "34", "18", "24", "24", "36", "12" ]	Number of squares mod n.
A000225	[ "0", "1", "3", "7", "15", "31", "63", "127", "255", "511", "1023", "2047", "4095", "8191", "16383", "32767", "65535", "131071", "262143", "524287", "1048575", "2097151", "4194303", "8388607", "16777215", "33554431", "67108863", "134217727", "268435455", "536870911", "1073741823", "2147483647", "4294967295", "8589934591" ]	a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
A000226	[ "1", "1", "3", "7", "18", "44", "117", "299", "793", "2095", "5607", "15047", "40708", "110499", "301541", "825784", "2270211", "6260800", "17319689", "48042494", "133606943", "372430476", "1040426154", "2912415527", "8167992598", "22947778342", "64577555147", "182009003773", "513729375064", "1452007713130" ]	Number of n-node unlabeled connected graphs with one cycle of length 3.
A000227	[ "1", "3", "7", "20", "55", "148", "403", "1097", "2981", "8103", "22026", "59874", "162755", "442413", "1202604", "3269017", "8886111", "24154953", "65659969", "178482301", "485165195", "1318815734", "3584912846", "9744803446", "26489122130", "72004899337", "195729609429", "532048240602", "1446257064291", "3931334297144", "10686474581524" ]	Nearest integer to e^n.
A000228	[ "1", "1", "3", "7", "22", "82", "333", "1448", "6572", "30490", "143552", "683101", "3274826", "15796897", "76581875", "372868101", "1822236628", "8934910362", "43939164263", "216651036012", "1070793308942" ]	Number of hexagonal polyominoes (or hexagonal polyforms, or planar polyhexes) with n cells.
A000229	[ "3", "7", "23", "71", "311", "479", "1559", "5711", "10559", "18191", "31391", "422231", "701399", "366791", "3818929", "9257329", "22000801", "36415991", "48473881", "175244281", "120293879", "427733329", "131486759", "3389934071", "2929911599", "7979490791", "36504256799", "23616331489", "89206899239", "121560956039" ]	a(n) is the least number m such that the n-th prime is the least quadratic nonresidue modulo m.
A000230	[ "2", "3", "7", "23", "89", "139", "199", "113", "1831", "523", "887", "1129", "1669", "2477", "2971", "4297", "5591", "1327", "9551", "30593", "19333", "16141", "15683", "81463", "28229", "31907", "19609", "35617", "82073", "44293", "43331", "34061", "89689", "162143", "134513", "173359", "31397", "404597", "212701", "188029", "542603", "265621", "461717", "155921", "544279", "404851", "927869", "1100977", "360653", "604073" ]	a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.
A000231	[ "2", "3", "7", "46", "4336", "134281216", "288230380379570176", "2658455991569831764110243006194384896", "452312848583266388373324160190187140390789016525312000869601987902398529536" ]	Number of inequivalent Boolean functions of n variables under action of complementing group.
A000232	[ "3", "8", "14", "14", "25", "24", "23", "22", "25", "59", "98", "97", "98", "97", "174", "176", "176", "176", "176", "291", "290", "289", "740", "874", "873", "872", "873", "872", "871", "870", "869", "868", "867", "866", "2180", "2179", "2178", "2177", "2771", "2770", "2769", "2768", "2767", "2766", "2765", "2764", "2763", "2763", "2763", "2763", "3366", "4208", "4207" ]	Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference).
A000233	[ "1", "3", "8", "16", "30", "46", "64", "96", "126", "158", "216", "256", "302", "396", "448", "512", "636", "702", "792", "960", "1052", "1118", "1344", "1472", "1550", "1866", "1944", "2048", "2442", "2540", "2688", "3072", "3212", "3388", "3888", "4032", "4094", "4746", "4928", "5056", "5832", "5852", "5976", "6912", "7020", "7180", "8064", "8192" ]	Generalized class numbers.
A000234	[ "1", "3", "8", "18", "37", "72", "136", "251", "445", "770", "1312", "2202", "3632", "5908", "9501", "15111", "23781", "37083", "57293", "87813", "133530", "201574", "302265", "450317", "666743", "981488", "1437003", "2092976", "3033253", "4375104", "6282026", "8981046", "12786327", "18131492", "25612628" ]	Partitions into non-integral powers (see Comments for precise definition).
A000235	[ "0", "0", "0", "1", "3", "8", "18", "38", "76", "147", "277", "509", "924", "1648", "2912", "5088", "8823", "15170", "25935", "44042", "74427", "125112", "209411", "348960", "579326", "958077", "1579098", "2593903", "4247768", "6935070", "11290627", "18330973", "29684082", "47946852", "77258764", "124198083" ]	Number of n-node rooted trees of height 3.
A000236	[ "3", "8", "20", "44", "80", "343", "288", "608", "1023", "2848", "4095", "40959", "16383", "32768", "11375", "655360", "262143", "3670016", "1048575", "2097151" ]	Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m).
A000237	[ "0", "1", "1", "3", "8", "26", "84", "297", "1066", "3976", "15093", "58426", "229189", "910127", "3649165", "14756491", "60103220", "246357081", "1015406251", "4205873378", "17497745509", "73084575666", "306352303774", "1288328048865", "5433980577776", "22982025183983" ]	Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.
A000238	[ "1", "1", "3", "8", "27", "91", "350", "1376", "5743", "24635", "108968", "492180", "2266502", "10598452", "50235931", "240872654", "1166732814", "5702001435", "28088787314", "139354922608", "695808554300", "3494390057212", "17641695461662", "89495023510876", "456009893224285", "2332997330210440" ]	Number of oriented trees with n nodes.
A000239	[ "1", "1", "3", "8", "28", "143", "933", "7150", "62310", "607445", "6545935", "77232740", "989893248", "13692587323", "203271723033", "3223180454138", "54362625941818", "971708196867905", "18347779304380995", "364911199401630640", "7624625589633857940", "166977535317365068775", "3824547112283439914893", "91440772473772839055238" ]	One-half of number of permutations of [n] with exactly one run of adjacent symbols differing by 1.
A000240	[ "1", "0", "3", "8", "45", "264", "1855", "14832", "133497", "1334960", "14684571", "176214840", "2290792933", "32071101048", "481066515735", "7697064251744", "130850092279665", "2355301661033952", "44750731559645107", "895014631192902120", "18795307255050944541", "413496759611120779880" ]	Rencontres numbers: number of permutations of [n] with exactly one fixed point.
A000241	[ "0", "0", "0", "0", "0", "1", "3", "9", "18", "36", "60", "100", "150" ]	Crossing number of complete graph with n nodes.
A000242	[ "1", "3", "9", "25", "69", "186", "503", "1353", "3651", "9865", "26748", "72729", "198447", "543159", "1491402", "4107152", "11342826", "31408719", "87189987", "242603970", "676524372", "1890436117", "5292722721", "14845095153", "41708679697", "117372283086", "330795842217" ]	3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees.
A000243	[ "1", "3", "9", "26", "75", "214", "612", "1747", "4995", "14294", "40967", "117560", "337830", "972027", "2800210", "8075889", "23315775", "67380458", "194901273", "564239262", "1634763697", "4739866803", "13752309730", "39926751310", "115988095896", "337138003197" ]	Number of trees with n nodes, 2 of which are labeled.
A000244	[ "1", "3", "9", "27", "81", "243", "729", "2187", "6561", "19683", "59049", "177147", "531441", "1594323", "4782969", "14348907", "43046721", "129140163", "387420489", "1162261467", "3486784401", "10460353203", "31381059609", "94143178827", "282429536481", "847288609443", "2541865828329", "7625597484987" ]	Powers of 3: a(n) = 3^n.
A000245	[ "0", "1", "3", "9", "28", "90", "297", "1001", "3432", "11934", "41990", "149226", "534888", "1931540", "7020405", "25662825", "94287120", "347993910", "1289624490", "4796857230", "17902146600", "67016296620", "251577050010", "946844533674", "3572042254128", "13505406670700", "51166197843852", "194214400834356" ]	a(n) = 3(2n)!/((n+2)!*(n-1)!).
A000246	[ "1", "1", "1", "3", "9", "45", "225", "1575", "11025", "99225", "893025", "9823275", "108056025", "1404728325", "18261468225", "273922023375", "4108830350625", "69850115960625", "1187451971330625", "22561587455281875", "428670161650355625", "9002073394657468125", "189043541287806830625" ]	Number of permutations in the symmetric group S_n that have odd order.
A000247	[ "0", "3", "10", "25", "56", "119", "246", "501", "1012", "2035", "4082", "8177", "16368", "32751", "65518", "131053", "262124", "524267", "1048554", "2097129", "4194280", "8388583", "16777190", "33554405", "67108836", "134217699", "268435426", "536870881", "1073741792", "2147483615" ]	a(n) = 2^n - n - 2.
A000248	[ "1", "1", "3", "10", "41", "196", "1057", "6322", "41393", "293608", "2237921", "18210094", "157329097", "1436630092", "13810863809", "139305550066", "1469959371233", "16184586405328", "185504221191745", "2208841954063318", "27272621155678841", "348586218389733556", "4605223387997411873" ]	Expansion of e.g.f. exp(x*exp(x)).
A000249	[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "10", "42", "193", "966", "5215", "30170", "186234", "1222065", "8496274", "62395234", "482700052", "3923995651", "33444263516", "298233514595", "2777192597789", "26959282453367", "272370017131462", "2859607460620573", "31156130591833647", "351808270089157421" ]	Nearest integer to modified Bessel function K_n(5).
A000250	[ "1", "3", "10", "45", "272", "2548", "39632", "1104306", "56871880", "5463113568", "978181717680", "326167542296048", "202701136710498400", "235284321080559981952", "511531711735594715527360", "2089424601541011618029114896", "16084004145036771186002041099712", "234026948449058790311618594954430848", "6454432593140577452393525511509194184320" ]	Number of symmetric reflexive relations on n nodes: (1/2)*A000666.
A000251	[ "1", "3", "11", "29", "74", "167", "367", "755", "1515", "2931", "5551", "10263", "18677", "33409", "59024", "102984", "177915", "304458", "516939", "871180", "1458882", "2428548", "4021670", "6627515", "10874462", "17770474", "28932739", "46943967", "75925797", "122433291", "196879385", "315759282", "505168033", "806290796", "1284034606", "2040485004", "3235965074", "5121801962", "8091411114", "12759606939", "20085832527", "31565046053", "49523414558", "77575278933", "121329065354", "189475663960", "295465391518", "460087656595", "715436020515", "1110994054004" ]	Number of trees of diameter 6.
A000252	[ "1", "6", "48", "96", "480", "288", "2016", "1536", "3888", "2880", "13200", "4608", "26208", "12096", "23040", "24576", "78336", "23328", "123120", "46080", "96768", "79200", "267168", "73728", "300000", "157248", "314928", "193536", "682080", "138240", "892800", "393216", "633600", "470016", "967680", "373248" ]	Number of invertible 2 X 2 matrices mod n.
A000253	[ "0", "1", "4", "11", "27", "63", "142", "312", "673", "1432", "3015", "6295", "13055", "26926", "55284", "113081", "230572", "468883", "951347", "1926527", "3894878", "7863152", "15855105", "31936240", "64269135", "129234351", "259690239", "521524126", "1046810092", "2100221753", "4212028452", "8444387067" ]	a(n) = 2*a(n-1) - a(n-2) + a(n-3) + 2^(n-1).
A000254	[ "0", "1", "3", "11", "50", "274", "1764", "13068", "109584", "1026576", "10628640", "120543840", "1486442880", "19802759040", "283465647360", "4339163001600", "70734282393600", "1223405590579200", "22376988058521600", "431565146817638400", "8752948036761600000", "186244810780170240000" ]	Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.
A000255	[ "1", "1", "3", "11", "53", "309", "2119", "16687", "148329", "1468457", "16019531", "190899411", "2467007773", "34361893981", "513137616783", "8178130767479", "138547156531409", "2486151753313617", "47106033220679059", "939765362752547227", "19690321886243846661", "432292066866171724421" ]	a(n) = na(n-1) + (n-1)a(n-2), a(0) = 1, a(1) = 1.
A000256	[ "1", "1", "0", "1", "3", "12", "52", "241", "1173", "5929", "30880", "164796", "897380", "4970296", "27930828", "158935761", "914325657", "5310702819", "31110146416", "183634501753", "1091371140915", "6526333259312", "39246152584304", "237214507388796", "1440503185260748" ]	Number of simple triangulations of the plane with n nodes.
A000257	[ "1", "1", "3", "12", "56", "288", "1584", "9152", "54912", "339456", "2149888", "13891584", "91287552", "608583680", "4107939840", "28030648320", "193100021760", "1341536993280", "9390758952960", "66182491668480", "469294031831040", "3346270487838720", "23981605162844160", "172667557172477952" ]	Number of rooted bicubic maps: a(n) = (8n-4)a(n-1)/(n+2) for n >= 2, a(0) = a(1) = 1.
A000258	[ "1", "1", "3", "12", "60", "358", "2471", "19302", "167894", "1606137", "16733779", "188378402", "2276423485", "29367807524", "402577243425", "5840190914957", "89345001017415", "1436904211547895", "24227076487779802", "427187837301557598", "7859930038606521508", "150601795280158255827" ]	Expansion of e.g.f. exp(exp(exp(x)-1)-1).
A000259	[ "1", "3", "13", "63", "326", "1761", "9808", "55895", "324301", "1908878", "11369744", "68395917", "414927215", "2535523154", "15592255913", "96419104103", "599176447614", "3739845108057", "23435007764606", "147374772979438", "929790132901804", "5883377105975922", "37328490926964481", "237427707464042693" ]	Number of certain rooted planar maps.
A000260	[ "1", "1", "3", "13", "68", "399", "2530", "16965", "118668", "857956", "6369883", "48336171", "373537388", "2931682810", "23317105140", "187606350645", "1524813969276", "12504654858828", "103367824774012", "860593023907540", "7211115497448720", "60776550501588855" ]	Number of rooted simplicial 3-polytopes with n+3 nodes; or rooted 3-connected triangulations with 2n+2 faces; or rooted 3-connected trivalent maps with 2n+2 vertices.
A000261	[ "0", "1", "3", "13", "71", "465", "3539", "30637", "296967", "3184129", "37401155", "477471021", "6581134823", "97388068753", "1539794649171", "25902759280525", "461904032857319", "8702813980639617", "172743930157869827", "3602826440828270029", "78768746000235327495", "1801366114380914335441" ]	a(n) = na(n-1) + (n-3)a(n-2), with a(1) = 0, a(2) = 1.
A000262	[ "1", "1", "3", "13", "73", "501", "4051", "37633", "394353", "4596553", "58941091", "824073141", "12470162233", "202976401213", "3535017524403", "65573803186921", "1290434218669921", "26846616451246353", "588633468315403843", "13564373693588558173", "327697927886085654441", "8281153039765859726341" ]	Number of "sets of lists": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset.
A000263	[ "3", "14", "39", "91", "173", "307", "502", "779", "1150", "1651", "2280", "3090", "4090", "5313", "6787", "8564", "10643", "13103", "15948", "19235", "23000", "27316", "32174", "37677", "43849", "50758", "58427", "66978", "76373", "86765", "98171", "110662", "124310", "139202", "155339", "172885" ]	Number of partitions into non-integral powers.
A000264	[ "1", "1", "3", "14", "80", "518", "3647", "27274", "213480", "1731652", "14455408", "123552488", "1077096124", "9548805240", "85884971043", "782242251522", "7203683481720", "66989439309452", "628399635777936", "5940930064989720", "56562734108608536" ]	Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle.
A000265	[ "1", "1", "3", "1", "5", "3", "7", "1", "9", "5", "11", "3", "13", "7", "15", "1", "17", "9", "19", "5", "21", "11", "23", "3", "25", "13", "27", "7", "29", "15", "31", "1", "33", "17", "35", "9", "37", "19", "39", "5", "41", "21", "43", "11", "45", "23", "47", "3", "49", "25", "51", "13", "53", "27", "55", "7", "57", "29", "59", "15", "61", "31", "63", "1", "65", "33", "67", "17", "69", "35", "71", "9", "73", "37", "75", "19", "77" ]	Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.
A000266	[ "1", "1", "1", "3", "15", "75", "435", "3045", "24465", "220185", "2200905", "24209955", "290529855", "3776888115", "52876298475", "793144477125", "12690313661025", "215735332237425", "3883235945814225", "73781482970470275", "1475629660064134575", "30988222861346826075", "681740902935880863075" ]	Expansion of e.g.f. exp(-x^2/2) / (1-x).
A000267	[ "1", "2", "3", "3", "4", "4", "5", "5", "5", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17" ]	Integer part of square root of 4n+1.
A000268	[ "1", "3", "15", "105", "947", "10472", "137337", "2085605", "36017472", "697407850", "14969626900", "352877606716", "9064191508018", "252024567201300", "7542036496650006", "241721880399970938", "8261159383595659128", "299916384730043070880", "11526945327529620432872", "467583770376898192016104" ]	E.g.f.: -log(1+log(1+log(1-x))).
A000269	[ "3", "16", "67", "251", "888", "3023", "10038", "32722", "105228", "334836", "1056611", "3311784", "10322791", "32026810", "98974177", "304835956", "936147219", "2867586542", "8764280567", "26733395986", "81399821915", "247459136331", "751211286356", "2277496842016" ]	Number of trees with n nodes, 3 of which are labeled.
A000270	[ "1", "1", "0", "3", "16", "95", "672", "5397", "48704", "487917", "5373920", "64547175", "839703696", "11762247419", "176509466560", "2825125339305", "48040633506048", "864932233294681", "16436901752820288", "328791893988472843", "6905593482159150480", "151941269284478380119", "3495011687269591273312" ]	For n >= 2, a(n) = b(n+1)+b(n)+b(n-1), where the b(i) are the ménage numbers A000179; a(0)=a(1)=1.
A000271	[ "1", "0", "0", "1", "3", "16", "96", "675", "5413", "48800", "488592", "5379333", "64595975", "840192288", "11767626752", "176574062535", "2825965531593", "48052401132800", "865108807357216", "16439727718351881", "328839946389605643", "6906458590966507696" ]	Sums of ménage numbers.
A000272	[ "1", "1", "1", "3", "16", "125", "1296", "16807", "262144", "4782969", "100000000", "2357947691", "61917364224", "1792160394037", "56693912375296", "1946195068359375", "72057594037927936", "2862423051509815793", "121439531096594251776", "5480386857784802185939" ]	Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
A000273	[ "1", "1", "3", "16", "218", "9608", "1540944", "882033440", "1793359192848", "13027956824399552", "341260431952972580352", "32522909385055886111197440", "11366745430825400574433894004224", "14669085692712929869037096075316220928", "70315656615234999521385506555979904091217920" ]	Number of unlabeled simple digraphs with n nodes.
A000274	[ "0", "0", "1", "3", "18", "110", "795", "6489", "59332", "600732", "6674805", "80765135", "1057289046", "14890154058", "224497707343", "3607998868005", "61576514013960", "1112225784377144", "21197714949305577", "425131949816628507", "8950146311929021210" ]	Number of permutations of length n with 2 consecutive ascending pairs.
A000275	[ "1", "1", "3", "19", "211", "3651", "90921", "3081513", "136407699", "7642177651", "528579161353", "44237263696473", "4405990782649369", "515018848029036937", "69818743428262376523", "10865441556038181291819", "1923889742567310611949459", "384565973956329859109177427", "86180438505835750284241676121" ]	Coefficients of a Bessel function (reciprocal of J_0(z)); also pairs of permutations with rise/rise forbidden.
A000276	[ "3", "20", "130", "924", "7308", "64224", "623376", "6636960", "76998240", "967524480", "13096736640", "190060335360", "2944310342400", "48503818137600", "846795372595200", "15618926924697600", "303517672703078400", "6198400928176128000", "132720966600284160000", "2973385109386137600000" ]	Associated Stirling numbers.
A000277	[ "1", "2", "5", "6", "9", "10", "13", "16", "17", "20", "23", "24", "27", "30", "33", "34", "37", "40", "43", "44", "47", "50", "53", "56", "57", "60", "63", "66", "69", "70", "73", "76", "79", "82", "85", "86", "89", "92", "95", "98", "101", "102", "105", "108", "111", "114", "117", "120", "121", "124", "127", "130", "133", "136", "139", "140", "143", "146", "149", "152", "155" ]	3n - 2floor(sqrt(4*n+5)) + 5.
A000278	[ "0", "1", "1", "2", "3", "7", "16", "65", "321", "4546", "107587", "20773703", "11595736272", "431558332068481", "134461531248108526465", "186242594112190847520182173826", "18079903385772308300945867582153787570051", "34686303861638264961101080464895364211215702792496667048327" ]	a(n) = a(n-1) + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
A000279	[ "3", "24", "216", "1824", "15150", "124416", "1014888", "8241792", "66724398", "538990800", "4346692680", "35009591040", "281699380560", "2264868936960", "18198009147600", "146142982814208", "1173123636533454", "9413509300965936", "75513633110271264", "605598295606296000", "4855626127979443908", "38924245740546950784" ]	Card matching: coefficients B[n,1] of t in the reduced hit polynomial A[n,n,n](t).
A000280	[ "0", "1", "1", "2", "3", "11", "38", "1369", "56241", "2565782650", "177895665388171", "16891164530321501264425013171", "5629840598310484749297545401724540333537382" ]	a(n) = a(n-1) + a(n-2)^3.
A000281	[ "1", "3", "57", "2763", "250737", "36581523", "7828053417", "2309644635483", "898621108880097", "445777636063460643", "274613643571568682777", "205676334188681975553003", "184053312545818735778213457", "193944394596325636374396208563" ]	Expansion of cos(x)/cos(2x).
A000282	[ "3", "70", "3783", "338475", "40565585", "6061961733", "1083852977811", "225615988054171", "53595807366038234", "14308700593468127485", "4241390625289880226714", "1382214286200071777573643", "491197439886557439295166226", "189044982636675290371386547592", "78334771617452038208125184627931", "34771576300926271400714044414858372" ]	Finite automata.
A000283	[ "0", "1", "1", "2", "5", "29", "866", "750797", "563696885165", "317754178345286893212434", "100967717855888389973004846476977145423449281581" ]	a(n) = a(n-1)^2 + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
A000284	[ "0", "1", "1", "2", "9", "731", "390617900", "59601394712394173339000731", "211723599072542785377729319366442939995427829921816290889198752331804918235791" ]	a(n) = a(n-1)^3 + a(n-2) with a(0)=0, a(1)=1.
A000285	[ "1", "4", "5", "9", "14", "23", "37", "60", "97", "157", "254", "411", "665", "1076", "1741", "2817", "4558", "7375", "11933", "19308", "31241", "50549", "81790", "132339", "214129", "346468", "560597", "907065", "1467662", "2374727", "3842389", "6217116", "10059505", "16276621", "26336126", "42612747", "68948873", "111561620", "180510493", "292072113", "472582606" ]	a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.
A000286	[ "0", "1", "1", "4", "5", "11", "20", "36", "65", "119", "218", "412", "770", "1466", "2784", "5322", "10226", "19691", "38048", "73665", "142927", "277822", "540851", "1054502", "2058507", "4023164", "7871226", "15414517", "30213010", "59266164", "116343183", "228545303", "449240025", "883569304", "1738768584", "3423466797", "6743729031" ]	Number of positive integers <= 2^n of form 2 x^2 + 5 y^2.
A000287	[ "1", "0", "4", "6", "24", "66", "214", "676", "2209", "7296", "24460", "82926", "284068", "981882", "3421318", "12007554", "42416488", "150718770", "538421590", "1932856590", "6969847486", "25237057110", "91729488354", "334589415276", "1224445617889", "4494622119424" ]	Number of rooted polyhedral graphs with n edges.
A000288	[ "1", "1", "1", "1", "4", "7", "13", "25", "49", "94", "181", "349", "673", "1297", "2500", "4819", "9289", "17905", "34513", "66526", "128233", "247177", "476449", "918385", "1770244", "3412255", "6577333", "12678217", "24438049", "47105854", "90799453", "175021573", "337364929", "650291809", "1253477764" ]	Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
A000289	[ "1", "4", "7", "31", "871", "756031", "571580604871", "326704387862983487112031", "106735757048926752040856495274871386126283608871", "11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031" ]	A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).
A000290	[ "0", "1", "4", "9", "16", "25", "36", "49", "64", "81", "100", "121", "144", "169", "196", "225", "256", "289", "324", "361", "400", "441", "484", "529", "576", "625", "676", "729", "784", "841", "900", "961", "1024", "1089", "1156", "1225", "1296", "1369", "1444", "1521", "1600", "1681", "1764", "1849", "1936", "2025", "2116", "2209", "2304", "2401", "2500" ]	The squares: a(n) = n^2.
A000291	[ "2", "4", "9", "16", "29", "47", "77", "118", "181", "267", "392", "560", "797", "1111", "1541", "2106", "2863", "3846", "5142", "6808", "8973", "11733", "15275", "19753", "25443", "32582", "41569", "52770", "66757", "84078", "105555", "131995", "164566", "204450", "253292", "312799", "385285", "473183", "579722", "708353", "863553" ]	Number of bipartite partitions of n white objects and 2 black ones.
A000292	[ "0", "1", "4", "10", "20", "35", "56", "84", "120", "165", "220", "286", "364", "455", "560", "680", "816", "969", "1140", "1330", "1540", "1771", "2024", "2300", "2600", "2925", "3276", "3654", "4060", "4495", "4960", "5456", "5984", "6545", "7140", "7770", "8436", "9139", "9880", "10660", "11480", "12341", "13244", "14190", "15180" ]	Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n(n+1)(n+2)/6.
A000293	[ "1", "1", "4", "10", "26", "59", "140", "307", "684", "1464", "3122", "6500", "13426", "27248", "54804", "108802", "214071", "416849", "805124", "1541637", "2930329", "5528733", "10362312", "19295226", "35713454", "65715094", "120256653", "218893580", "396418699", "714399381", "1281403841", "2287986987", "4067428375", "7200210523", "12693890803", "22290727268", "38993410516", "67959010130", "118016656268", "204233654229", "352245710866", "605538866862", "1037668522922", "1772700955975", "3019333854177", "5127694484375", "8683676638832", "14665233966068", "24700752691832", "41495176877972", "69531305679518" ]	a(n) = number of solid (i.e., three-dimensional) partitions of n.
A000294	[ "1", "1", "4", "10", "26", "59", "141", "310", "692", "1483", "3162", "6583", "13602", "27613", "55579", "110445", "217554", "424148", "820294", "1572647", "2992892", "5652954", "10605608", "19765082", "36609945", "67405569", "123412204", "224728451", "407119735", "733878402", "1316631730", "2351322765", "4180714647", "7401898452", "13051476707", "22922301583", "40105025130", "69909106888", "121427077241", "210179991927", "362583131144" ]	Expansion of g.f. Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).
A000295	[ "0", "0", "1", "4", "11", "26", "57", "120", "247", "502", "1013", "2036", "4083", "8178", "16369", "32752", "65519", "131054", "262125", "524268", "1048555", "2097130", "4194281", "8388584", "16777191", "33554406", "67108837", "134217700", "268435427", "536870882", "1073741793", "2147483616", "4294967263", "8589934558" ]	Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018).
A000296	[ "1", "0", "1", "1", "4", "11", "41", "162", "715", "3425", "17722", "98253", "580317", "3633280", "24011157", "166888165", "1216070380", "9264071767", "73600798037", "608476008122", "5224266196935", "46499892038437", "428369924118314", "4078345814329009", "40073660040755337", "405885209254049952", "4232705122975949401" ]	Set partitions without singletons: number of partitions of an n-set into blocks of size > 1. Also number of cyclically spaced (or feasible) partitions.
A000297	[ "0", "4", "12", "25", "44", "70", "104", "147", "200", "264", "340", "429", "532", "650", "784", "935", "1104", "1292", "1500", "1729", "1980", "2254", "2552", "2875", "3224", "3600", "4004", "4437", "4900", "5394", "5920", "6479", "7072", "7700", "8364", "9065", "9804", "10582", "11400", "12259", "13160", "14104", "15092", "16125", "17204" ]	a(n) = (n+1)(n+3)(n+8)/6.
A000298	[ "1", "4", "12", "30", "70", "159", "339", "706", "1436", "2853", "5551", "10622", "19975", "37043", "67811", "122561", "219090", "387578", "678977", "1178769", "2029115", "3465056", "5872648", "9882301", "16517284", "27430358", "45275673", "74297072", "121245153", "196810381", "317850809", "510830685", "817139589", "1301251186", "2063204707", "3257690903", "5123047561" ]	Number of partitions into non-integral powers.
A000299	[ "0", "0", "0", "0", "1", "4", "13", "36", "93", "225", "528", "1198", "2666", "5815", "12517", "26587", "55933", "116564", "241151", "495417", "1011950", "2055892", "4157514", "8371318", "16792066", "33564256", "66875221", "132849983", "263192599", "520087551", "1025295487", "2016745784", "3958608430", "7754810743" ]	Number of n-node rooted trees of height 4.
A000300	[ "1", "4", "14", "44", "133", "388", "1116", "3168", "8938", "25100", "70334", "196824", "550656", "1540832", "4314190", "12089368", "33911543", "95228760", "267727154", "753579420", "2123637318", "5991571428", "16923929406", "47857425416", "135478757308", "383929643780", "1089118243128", "3092612497260" ]	4th power of rooted tree enumerator: linear forests of 4 rooted trees.

A000201

[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "33", "35", "37", "38", "40", "42", "43", "45", "46", "48", "50", "51", "53", "55", "56", "58", "59", "61", "63", "64", "66", "67", "69", "71", "72", "74", "76", "77", "79", "80", "82", "84", "85", "87", "88", "90", "92", "93", "95", "97", "98", "100", "101", "103", "105", "106", "108", "110" ]

Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.

A000202

[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "34", "35", "37", "38", "40", "42", "43", "45", "47", "48", "50", "51", "53", "55", "56", "58", "60", "61", "63", "64", "66", "68", "69", "71", "73", "74", "76", "77", "79", "81", "82", "84", "86", "87", "89", "90", "92", "94", "95", "97", "99", "100", "102", "103", "105", "107", "108", "110" ]

a(8i+j) = 13i + a(j), where 1<=j<=8.

A000203

[ "1", "3", "4", "7", "6", "12", "8", "15", "13", "18", "12", "28", "14", "24", "24", "31", "18", "39", "20", "42", "32", "36", "24", "60", "31", "42", "40", "56", "30", "72", "32", "63", "48", "54", "48", "91", "38", "60", "56", "90", "42", "96", "44", "84", "78", "72", "48", "124", "57", "93", "72", "98", "54", "120", "72", "120", "80", "90", "60", "168", "62", "96", "104", "127", "84", "144", "68", "126", "96", "144" ]

a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).

A000204

[ "1", "3", "4", "7", "11", "18", "29", "47", "76", "123", "199", "322", "521", "843", "1364", "2207", "3571", "5778", "9349", "15127", "24476", "39603", "64079", "103682", "167761", "271443", "439204", "710647", "1149851", "1860498", "3010349", "4870847", "7881196", "12752043", "20633239", "33385282", "54018521", "87403803", "141422324" ]

Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.

A000205

[ "1", "1", "3", "4", "8", "14", "25", "45", "82", "151", "282", "531", "1003", "1907", "3645", "6993", "13456", "25978", "50248", "97446", "189291", "368338", "717804", "1400699", "2736534", "5352182", "10478044", "20531668", "40264582", "79022464", "155196838", "304997408", "599752463", "1180027022", "2322950591", "4575114295" ]

Number of positive integers <= 2^n of form x^2 + 3 y^2.

A000206

[ "1", "1", "3", "4", "12", "22", "71", "181", "618", "1957", "6966", "24367", "89010", "324766", "1204815", "4482400", "16802826", "63195016", "238711285", "904338163", "3436380192", "13089961012", "49979421837", "191221556269", "733014218506", "2814758323498", "10825986453978", "41700030726757", "160842946895004" ]

Even sequences with period 2n.

A000207

[ "1", "1", "1", "3", "4", "12", "27", "82", "228", "733", "2282", "7528", "24834", "83898", "285357", "983244", "3412420", "11944614", "42080170", "149197152", "531883768", "1905930975", "6861221666", "24806004996", "90036148954", "327989004892", "1198854697588", "4395801203290", "16165198379984", "59609171366326", "220373278174641" ]

Number of inequivalent ways of dissecting a regular (n+2)-gon into n triangles by n-1 non-intersecting diagonals under rotations and reflections; also the number of planar 2-trees.

A000208

[ "1", "1", "3", "4", "12", "28", "94", "298", "1044", "3658", "13164", "47710", "174948", "645436", "2397342", "8948416", "33556500", "126324496", "477225962", "1808414182", "6871973952", "26178873448", "99955697946", "382438918234", "1466015854100", "5629499869780" ]

Number of even sequences with period 2n.

A000209

[ "0", "2", "-2", "0", "1", "-3", "0", "1", "-7", "0", "1", "-226", "-1", "0", "7", "-1", "0", "3", "-1", "0", "2", "-2", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-75", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-45", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-32", "-1", "0", "9", "-1" ]

Nearest integer to tan n.

A000210

[ "1", "3", "5", "6", "8", "10", "12", "13", "15", "17", "18", "20", "22", "24", "25", "27", "29", "30", "32", "34", "36", "37", "39", "41", "42", "44", "46", "48", "49", "51", "53", "54", "56", "58", "60", "61", "63", "65", "67", "68", "70", "72", "73", "75", "77", "79", "80", "82", "84", "85", "87", "89", "91", "92", "94", "96", "97", "99", "101", "103", "104", "106", "108", "109", "111", "113", "115", "116" ]

A Beatty sequence: floor(n*(e-1)).

A000211

[ "4", "3", "5", "6", "9", "13", "20", "31", "49", "78", "125", "201", "324", "523", "845", "1366", "2209", "3573", "5780", "9351", "15129", "24478", "39605", "64081", "103684", "167763", "271445", "439206", "710649", "1149853", "1860500", "3010351", "4870849", "7881198" ]

a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.

A000212

[ "0", "0", "1", "3", "5", "8", "12", "16", "21", "27", "33", "40", "48", "56", "65", "75", "85", "96", "108", "120", "133", "147", "161", "176", "192", "208", "225", "243", "261", "280", "300", "320", "341", "363", "385", "408", "432", "456", "481", "507", "533", "560", "588", "616", "645", "675", "705", "736", "768", "800", "833", "867", "901", "936" ]

a(n) = floor(n^2/3).

A000213

[ "1", "1", "1", "3", "5", "9", "17", "31", "57", "105", "193", "355", "653", "1201", "2209", "4063", "7473", "13745", "25281", "46499", "85525", "157305", "289329", "532159", "978793", "1800281", "3311233", "6090307", "11201821", "20603361", "37895489", "69700671", "128199521", "235795681", "433695873", "797691075", "1467182629" ]

Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.

A000214

[ "3", "5", "10", "32", "382", "15768919", "16224999167506438730294", "84575066435667906978109556031081616704183639810103015118" ]

Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).

A000215

[ "3", "5", "17", "257", "65537", "4294967297", "18446744073709551617", "340282366920938463463374607431768211457", "115792089237316195423570985008687907853269984665640564039457584007913129639937" ]

Fermat numbers: a(n) = 2^(2^n) + 1.

A000216

[ "2", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]

Take sum of squares of digits of previous term, starting with 2.

A000217

[ "0", "1", "3", "6", "10", "15", "21", "28", "36", "45", "55", "66", "78", "91", "105", "120", "136", "153", "171", "190", "210", "231", "253", "276", "300", "325", "351", "378", "406", "435", "465", "496", "528", "561", "595", "630", "666", "703", "741", "780", "820", "861", "903", "946", "990", "1035", "1081", "1128", "1176", "1225", "1275", "1326", "1378", "1431" ]

Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.

A000218

[ "3", "9", "81", "65", "61", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]

Take sum of squares of digits of previous term; start with 3.

A000219

[ "1", "1", "3", "6", "13", "24", "48", "86", "160", "282", "500", "859", "1479", "2485", "4167", "6879", "11297", "18334", "29601", "47330", "75278", "118794", "186475", "290783", "451194", "696033", "1068745", "1632658", "2483234", "3759612", "5668963", "8512309", "12733429", "18974973", "28175955", "41691046", "61484961", "90379784", "132441995", "193487501", "281846923" ]

Number of planar partitions (or plane partitions) of n.

A000220

[ "1", "0", "0", "0", "0", "0", "1", "1", "3", "6", "15", "29", "67", "139", "310", "667", "1480", "3244", "7241", "16104", "36192", "81435", "184452", "418870", "955860", "2187664", "5025990", "11580130", "26765230", "62027433", "144133676", "335731381", "783859852", "1834104934", "4300433063", "10102854473", "23778351222" ]

Number of asymmetric trees with n nodes (also called identity trees).

A000221

[ "5", "25", "29", "85", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145" ]

Take sum of squares of digits of previous term; start with 5.

A000222

[ "0", "0", "1", "3", "6", "38", "213", "1479", "11692", "104364", "1036809", "11344859", "135548466", "1755739218", "24504637741", "366596136399", "5852040379224", "99283915922264", "1783921946910417", "33840669046326579", "675849838112277598", "14174636583759324798" ]

Coefficients of ménage hit polynomials.

A000223

[ "3", "7", "10", "19", "32", "34", "37", "51", "81", "119", "122", "134", "157", "160", "161", "174", "221", "252", "254", "294", "305", "309", "364", "371", "405", "580", "682", "734", "756", "763", "776", "959", "1028", "1105", "1120", "1170", "1205", "1550", "1570", "1576", "1851", "1930", "2028", "2404", "2411", "2565", "2675", "2895", "2905", "2940", "3133", "3211", "3240", "3428" ]

Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).

A000224

[ "1", "2", "2", "2", "3", "4", "4", "3", "4", "6", "6", "4", "7", "8", "6", "4", "9", "8", "10", "6", "8", "12", "12", "6", "11", "14", "11", "8", "15", "12", "16", "7", "12", "18", "12", "8", "19", "20", "14", "9", "21", "16", "22", "12", "12", "24", "24", "8", "22", "22", "18", "14", "27", "22", "18", "12", "20", "30", "30", "12", "31", "32", "16", "12", "21", "24", "34", "18", "24", "24", "36", "12" ]

Number of squares mod n.

A000225

[ "0", "1", "3", "7", "15", "31", "63", "127", "255", "511", "1023", "2047", "4095", "8191", "16383", "32767", "65535", "131071", "262143", "524287", "1048575", "2097151", "4194303", "8388607", "16777215", "33554431", "67108863", "134217727", "268435455", "536870911", "1073741823", "2147483647", "4294967295", "8589934591" ]

a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)

A000226

[ "1", "1", "3", "7", "18", "44", "117", "299", "793", "2095", "5607", "15047", "40708", "110499", "301541", "825784", "2270211", "6260800", "17319689", "48042494", "133606943", "372430476", "1040426154", "2912415527", "8167992598", "22947778342", "64577555147", "182009003773", "513729375064", "1452007713130" ]

Number of n-node unlabeled connected graphs with one cycle of length 3.

A000227

[ "1", "3", "7", "20", "55", "148", "403", "1097", "2981", "8103", "22026", "59874", "162755", "442413", "1202604", "3269017", "8886111", "24154953", "65659969", "178482301", "485165195", "1318815734", "3584912846", "9744803446", "26489122130", "72004899337", "195729609429", "532048240602", "1446257064291", "3931334297144", "10686474581524" ]

Nearest integer to e^n.

A000228

[ "1", "1", "3", "7", "22", "82", "333", "1448", "6572", "30490", "143552", "683101", "3274826", "15796897", "76581875", "372868101", "1822236628", "8934910362", "43939164263", "216651036012", "1070793308942" ]

Number of hexagonal polyominoes (or hexagonal polyforms, or planar polyhexes) with n cells.

A000229

[ "3", "7", "23", "71", "311", "479", "1559", "5711", "10559", "18191", "31391", "422231", "701399", "366791", "3818929", "9257329", "22000801", "36415991", "48473881", "175244281", "120293879", "427733329", "131486759", "3389934071", "2929911599", "7979490791", "36504256799", "23616331489", "89206899239", "121560956039" ]

a(n) is the least number m such that the n-th prime is the least quadratic nonresidue modulo m.

A000230

[ "2", "3", "7", "23", "89", "139", "199", "113", "1831", "523", "887", "1129", "1669", "2477", "2971", "4297", "5591", "1327", "9551", "30593", "19333", "16141", "15683", "81463", "28229", "31907", "19609", "35617", "82073", "44293", "43331", "34061", "89689", "162143", "134513", "173359", "31397", "404597", "212701", "188029", "542603", "265621", "461717", "155921", "544279", "404851", "927869", "1100977", "360653", "604073" ]

a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.

A000231

[ "2", "3", "7", "46", "4336", "134281216", "288230380379570176", "2658455991569831764110243006194384896", "452312848583266388373324160190187140390789016525312000869601987902398529536" ]

Number of inequivalent Boolean functions of n variables under action of complementing group.

A000232

[ "3", "8", "14", "14", "25", "24", "23", "22", "25", "59", "98", "97", "98", "97", "174", "176", "176", "176", "176", "291", "290", "289", "740", "874", "873", "872", "873", "872", "871", "870", "869", "868", "867", "866", "2180", "2179", "2178", "2177", "2771", "2770", "2769", "2768", "2767", "2766", "2765", "2764", "2763", "2763", "2763", "2763", "3366", "4208", "4207" ]

Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference).

A000233

[ "1", "3", "8", "16", "30", "46", "64", "96", "126", "158", "216", "256", "302", "396", "448", "512", "636", "702", "792", "960", "1052", "1118", "1344", "1472", "1550", "1866", "1944", "2048", "2442", "2540", "2688", "3072", "3212", "3388", "3888", "4032", "4094", "4746", "4928", "5056", "5832", "5852", "5976", "6912", "7020", "7180", "8064", "8192" ]

Generalized class numbers.

A000234

[ "1", "3", "8", "18", "37", "72", "136", "251", "445", "770", "1312", "2202", "3632", "5908", "9501", "15111", "23781", "37083", "57293", "87813", "133530", "201574", "302265", "450317", "666743", "981488", "1437003", "2092976", "3033253", "4375104", "6282026", "8981046", "12786327", "18131492", "25612628" ]

Partitions into non-integral powers (see Comments for precise definition).

A000235

[ "0", "0", "0", "1", "3", "8", "18", "38", "76", "147", "277", "509", "924", "1648", "2912", "5088", "8823", "15170", "25935", "44042", "74427", "125112", "209411", "348960", "579326", "958077", "1579098", "2593903", "4247768", "6935070", "11290627", "18330973", "29684082", "47946852", "77258764", "124198083" ]

Number of n-node rooted trees of height 3.

A000236

[ "3", "8", "20", "44", "80", "343", "288", "608", "1023", "2848", "4095", "40959", "16383", "32768", "11375", "655360", "262143", "3670016", "1048575", "2097151" ]

Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m).

A000237

[ "0", "1", "1", "3", "8", "26", "84", "297", "1066", "3976", "15093", "58426", "229189", "910127", "3649165", "14756491", "60103220", "246357081", "1015406251", "4205873378", "17497745509", "73084575666", "306352303774", "1288328048865", "5433980577776", "22982025183983" ]

Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.

A000238

[ "1", "1", "3", "8", "27", "91", "350", "1376", "5743", "24635", "108968", "492180", "2266502", "10598452", "50235931", "240872654", "1166732814", "5702001435", "28088787314", "139354922608", "695808554300", "3494390057212", "17641695461662", "89495023510876", "456009893224285", "2332997330210440" ]

Number of oriented trees with n nodes.

A000239

[ "1", "1", "3", "8", "28", "143", "933", "7150", "62310", "607445", "6545935", "77232740", "989893248", "13692587323", "203271723033", "3223180454138", "54362625941818", "971708196867905", "18347779304380995", "364911199401630640", "7624625589633857940", "166977535317365068775", "3824547112283439914893", "91440772473772839055238" ]

One-half of number of permutations of [n] with exactly one run of adjacent symbols differing by 1.

A000240

[ "1", "0", "3", "8", "45", "264", "1855", "14832", "133497", "1334960", "14684571", "176214840", "2290792933", "32071101048", "481066515735", "7697064251744", "130850092279665", "2355301661033952", "44750731559645107", "895014631192902120", "18795307255050944541", "413496759611120779880" ]

Rencontres numbers: number of permutations of [n] with exactly one fixed point.

A000241

[ "0", "0", "0", "0", "0", "1", "3", "9", "18", "36", "60", "100", "150" ]

Crossing number of complete graph with n nodes.

A000242

[ "1", "3", "9", "25", "69", "186", "503", "1353", "3651", "9865", "26748", "72729", "198447", "543159", "1491402", "4107152", "11342826", "31408719", "87189987", "242603970", "676524372", "1890436117", "5292722721", "14845095153", "41708679697", "117372283086", "330795842217" ]

3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees.

A000243

[ "1", "3", "9", "26", "75", "214", "612", "1747", "4995", "14294", "40967", "117560", "337830", "972027", "2800210", "8075889", "23315775", "67380458", "194901273", "564239262", "1634763697", "4739866803", "13752309730", "39926751310", "115988095896", "337138003197" ]

Number of trees with n nodes, 2 of which are labeled.

A000244

[ "1", "3", "9", "27", "81", "243", "729", "2187", "6561", "19683", "59049", "177147", "531441", "1594323", "4782969", "14348907", "43046721", "129140163", "387420489", "1162261467", "3486784401", "10460353203", "31381059609", "94143178827", "282429536481", "847288609443", "2541865828329", "7625597484987" ]

Powers of 3: a(n) = 3^n.

A000245

[ "0", "1", "3", "9", "28", "90", "297", "1001", "3432", "11934", "41990", "149226", "534888", "1931540", "7020405", "25662825", "94287120", "347993910", "1289624490", "4796857230", "17902146600", "67016296620", "251577050010", "946844533674", "3572042254128", "13505406670700", "51166197843852", "194214400834356" ]

a(n) = 3*(2*n)!/((n+2)!*(n-1)!).

A000246

[ "1", "1", "1", "3", "9", "45", "225", "1575", "11025", "99225", "893025", "9823275", "108056025", "1404728325", "18261468225", "273922023375", "4108830350625", "69850115960625", "1187451971330625", "22561587455281875", "428670161650355625", "9002073394657468125", "189043541287806830625" ]

Number of permutations in the symmetric group S_n that have odd order.

A000247

[ "0", "3", "10", "25", "56", "119", "246", "501", "1012", "2035", "4082", "8177", "16368", "32751", "65518", "131053", "262124", "524267", "1048554", "2097129", "4194280", "8388583", "16777190", "33554405", "67108836", "134217699", "268435426", "536870881", "1073741792", "2147483615" ]

a(n) = 2^n - n - 2.

A000248

[ "1", "1", "3", "10", "41", "196", "1057", "6322", "41393", "293608", "2237921", "18210094", "157329097", "1436630092", "13810863809", "139305550066", "1469959371233", "16184586405328", "185504221191745", "2208841954063318", "27272621155678841", "348586218389733556", "4605223387997411873" ]

Expansion of e.g.f. exp(x*exp(x)).

A000249

[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "10", "42", "193", "966", "5215", "30170", "186234", "1222065", "8496274", "62395234", "482700052", "3923995651", "33444263516", "298233514595", "2777192597789", "26959282453367", "272370017131462", "2859607460620573", "31156130591833647", "351808270089157421" ]

Nearest integer to modified Bessel function K_n(5).

A000250

[ "1", "3", "10", "45", "272", "2548", "39632", "1104306", "56871880", "5463113568", "978181717680", "326167542296048", "202701136710498400", "235284321080559981952", "511531711735594715527360", "2089424601541011618029114896", "16084004145036771186002041099712", "234026948449058790311618594954430848", "6454432593140577452393525511509194184320" ]

Number of symmetric reflexive relations on n nodes: (1/2)*A000666.

A000251

[ "1", "3", "11", "29", "74", "167", "367", "755", "1515", "2931", "5551", "10263", "18677", "33409", "59024", "102984", "177915", "304458", "516939", "871180", "1458882", "2428548", "4021670", "6627515", "10874462", "17770474", "28932739", "46943967", "75925797", "122433291", "196879385", "315759282", "505168033", "806290796", "1284034606", "2040485004", "3235965074", "5121801962", "8091411114", "12759606939", "20085832527", "31565046053", "49523414558", "77575278933", "121329065354", "189475663960", "295465391518", "460087656595", "715436020515", "1110994054004" ]

Number of trees of diameter 6.

A000252

[ "1", "6", "48", "96", "480", "288", "2016", "1536", "3888", "2880", "13200", "4608", "26208", "12096", "23040", "24576", "78336", "23328", "123120", "46080", "96768", "79200", "267168", "73728", "300000", "157248", "314928", "193536", "682080", "138240", "892800", "393216", "633600", "470016", "967680", "373248" ]

Number of invertible 2 X 2 matrices mod n.

A000253

[ "0", "1", "4", "11", "27", "63", "142", "312", "673", "1432", "3015", "6295", "13055", "26926", "55284", "113081", "230572", "468883", "951347", "1926527", "3894878", "7863152", "15855105", "31936240", "64269135", "129234351", "259690239", "521524126", "1046810092", "2100221753", "4212028452", "8444387067" ]

a(n) = 2*a(n-1) - a(n-2) + a(n-3) + 2^(n-1).

A000254

[ "0", "1", "3", "11", "50", "274", "1764", "13068", "109584", "1026576", "10628640", "120543840", "1486442880", "19802759040", "283465647360", "4339163001600", "70734282393600", "1223405590579200", "22376988058521600", "431565146817638400", "8752948036761600000", "186244810780170240000" ]

Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.

A000255

[ "1", "1", "3", "11", "53", "309", "2119", "16687", "148329", "1468457", "16019531", "190899411", "2467007773", "34361893981", "513137616783", "8178130767479", "138547156531409", "2486151753313617", "47106033220679059", "939765362752547227", "19690321886243846661", "432292066866171724421" ]

a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.

A000256

[ "1", "1", "0", "1", "3", "12", "52", "241", "1173", "5929", "30880", "164796", "897380", "4970296", "27930828", "158935761", "914325657", "5310702819", "31110146416", "183634501753", "1091371140915", "6526333259312", "39246152584304", "237214507388796", "1440503185260748" ]

Number of simple triangulations of the plane with n nodes.

A000257

[ "1", "1", "3", "12", "56", "288", "1584", "9152", "54912", "339456", "2149888", "13891584", "91287552", "608583680", "4107939840", "28030648320", "193100021760", "1341536993280", "9390758952960", "66182491668480", "469294031831040", "3346270487838720", "23981605162844160", "172667557172477952" ]

Number of rooted bicubic maps: a(n) = (8*n-4)*a(n-1)/(n+2) for n >= 2, a(0) = a(1) = 1.

A000258

[ "1", "1", "3", "12", "60", "358", "2471", "19302", "167894", "1606137", "16733779", "188378402", "2276423485", "29367807524", "402577243425", "5840190914957", "89345001017415", "1436904211547895", "24227076487779802", "427187837301557598", "7859930038606521508", "150601795280158255827" ]

Expansion of e.g.f. exp(exp(exp(x)-1)-1).

A000259

[ "1", "3", "13", "63", "326", "1761", "9808", "55895", "324301", "1908878", "11369744", "68395917", "414927215", "2535523154", "15592255913", "96419104103", "599176447614", "3739845108057", "23435007764606", "147374772979438", "929790132901804", "5883377105975922", "37328490926964481", "237427707464042693" ]

Number of certain rooted planar maps.

A000260

[ "1", "1", "3", "13", "68", "399", "2530", "16965", "118668", "857956", "6369883", "48336171", "373537388", "2931682810", "23317105140", "187606350645", "1524813969276", "12504654858828", "103367824774012", "860593023907540", "7211115497448720", "60776550501588855" ]

Number of rooted simplicial 3-polytopes with n+3 nodes; or rooted 3-connected triangulations with 2n+2 faces; or rooted 3-connected trivalent maps with 2n+2 vertices.

A000261

[ "0", "1", "3", "13", "71", "465", "3539", "30637", "296967", "3184129", "37401155", "477471021", "6581134823", "97388068753", "1539794649171", "25902759280525", "461904032857319", "8702813980639617", "172743930157869827", "3602826440828270029", "78768746000235327495", "1801366114380914335441" ]

a(n) = n*a(n-1) + (n-3)*a(n-2), with a(1) = 0, a(2) = 1.

A000262

[ "1", "1", "3", "13", "73", "501", "4051", "37633", "394353", "4596553", "58941091", "824073141", "12470162233", "202976401213", "3535017524403", "65573803186921", "1290434218669921", "26846616451246353", "588633468315403843", "13564373693588558173", "327697927886085654441", "8281153039765859726341" ]

Number of "sets of lists": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset.

A000263

[ "3", "14", "39", "91", "173", "307", "502", "779", "1150", "1651", "2280", "3090", "4090", "5313", "6787", "8564", "10643", "13103", "15948", "19235", "23000", "27316", "32174", "37677", "43849", "50758", "58427", "66978", "76373", "86765", "98171", "110662", "124310", "139202", "155339", "172885" ]

Number of partitions into non-integral powers.

A000264

[ "1", "1", "3", "14", "80", "518", "3647", "27274", "213480", "1731652", "14455408", "123552488", "1077096124", "9548805240", "85884971043", "782242251522", "7203683481720", "66989439309452", "628399635777936", "5940930064989720", "56562734108608536" ]

Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle.

A000265

[ "1", "1", "3", "1", "5", "3", "7", "1", "9", "5", "11", "3", "13", "7", "15", "1", "17", "9", "19", "5", "21", "11", "23", "3", "25", "13", "27", "7", "29", "15", "31", "1", "33", "17", "35", "9", "37", "19", "39", "5", "41", "21", "43", "11", "45", "23", "47", "3", "49", "25", "51", "13", "53", "27", "55", "7", "57", "29", "59", "15", "61", "31", "63", "1", "65", "33", "67", "17", "69", "35", "71", "9", "73", "37", "75", "19", "77" ]

Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.

A000266

[ "1", "1", "1", "3", "15", "75", "435", "3045", "24465", "220185", "2200905", "24209955", "290529855", "3776888115", "52876298475", "793144477125", "12690313661025", "215735332237425", "3883235945814225", "73781482970470275", "1475629660064134575", "30988222861346826075", "681740902935880863075" ]

Expansion of e.g.f. exp(-x^2/2) / (1-x).

A000267

[ "1", "2", "3", "3", "4", "4", "5", "5", "5", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17" ]

Integer part of square root of 4n+1.

A000268

[ "1", "3", "15", "105", "947", "10472", "137337", "2085605", "36017472", "697407850", "14969626900", "352877606716", "9064191508018", "252024567201300", "7542036496650006", "241721880399970938", "8261159383595659128", "299916384730043070880", "11526945327529620432872", "467583770376898192016104" ]

E.g.f.: -log(1+log(1+log(1-x))).

A000269

[ "3", "16", "67", "251", "888", "3023", "10038", "32722", "105228", "334836", "1056611", "3311784", "10322791", "32026810", "98974177", "304835956", "936147219", "2867586542", "8764280567", "26733395986", "81399821915", "247459136331", "751211286356", "2277496842016" ]

Number of trees with n nodes, 3 of which are labeled.

A000270

[ "1", "1", "0", "3", "16", "95", "672", "5397", "48704", "487917", "5373920", "64547175", "839703696", "11762247419", "176509466560", "2825125339305", "48040633506048", "864932233294681", "16436901752820288", "328791893988472843", "6905593482159150480", "151941269284478380119", "3495011687269591273312" ]

For n >= 2, a(n) = b(n+1)+b(n)+b(n-1), where the b(i) are the ménage numbers A000179; a(0)=a(1)=1.

A000271

[ "1", "0", "0", "1", "3", "16", "96", "675", "5413", "48800", "488592", "5379333", "64595975", "840192288", "11767626752", "176574062535", "2825965531593", "48052401132800", "865108807357216", "16439727718351881", "328839946389605643", "6906458590966507696" ]

Sums of ménage numbers.

A000272

[ "1", "1", "1", "3", "16", "125", "1296", "16807", "262144", "4782969", "100000000", "2357947691", "61917364224", "1792160394037", "56693912375296", "1946195068359375", "72057594037927936", "2862423051509815793", "121439531096594251776", "5480386857784802185939" ]

Number of trees on n labeled nodes: n^(n-2) with a(0)=1.

A000273

[ "1", "1", "3", "16", "218", "9608", "1540944", "882033440", "1793359192848", "13027956824399552", "341260431952972580352", "32522909385055886111197440", "11366745430825400574433894004224", "14669085692712929869037096075316220928", "70315656615234999521385506555979904091217920" ]

Number of unlabeled simple digraphs with n nodes.

A000274

[ "0", "0", "1", "3", "18", "110", "795", "6489", "59332", "600732", "6674805", "80765135", "1057289046", "14890154058", "224497707343", "3607998868005", "61576514013960", "1112225784377144", "21197714949305577", "425131949816628507", "8950146311929021210" ]

Number of permutations of length n with 2 consecutive ascending pairs.

A000275

[ "1", "1", "3", "19", "211", "3651", "90921", "3081513", "136407699", "7642177651", "528579161353", "44237263696473", "4405990782649369", "515018848029036937", "69818743428262376523", "10865441556038181291819", "1923889742567310611949459", "384565973956329859109177427", "86180438505835750284241676121" ]

Coefficients of a Bessel function (reciprocal of J_0(z)); also pairs of permutations with rise/rise forbidden.

A000276

[ "3", "20", "130", "924", "7308", "64224", "623376", "6636960", "76998240", "967524480", "13096736640", "190060335360", "2944310342400", "48503818137600", "846795372595200", "15618926924697600", "303517672703078400", "6198400928176128000", "132720966600284160000", "2973385109386137600000" ]

Associated Stirling numbers.

A000277

[ "1", "2", "5", "6", "9", "10", "13", "16", "17", "20", "23", "24", "27", "30", "33", "34", "37", "40", "43", "44", "47", "50", "53", "56", "57", "60", "63", "66", "69", "70", "73", "76", "79", "82", "85", "86", "89", "92", "95", "98", "101", "102", "105", "108", "111", "114", "117", "120", "121", "124", "127", "130", "133", "136", "139", "140", "143", "146", "149", "152", "155" ]

3*n - 2*floor(sqrt(4*n+5)) + 5.

A000278

[ "0", "1", "1", "2", "3", "7", "16", "65", "321", "4546", "107587", "20773703", "11595736272", "431558332068481", "134461531248108526465", "186242594112190847520182173826", "18079903385772308300945867582153787570051", "34686303861638264961101080464895364211215702792496667048327" ]

a(n) = a(n-1) + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.

A000279

[ "3", "24", "216", "1824", "15150", "124416", "1014888", "8241792", "66724398", "538990800", "4346692680", "35009591040", "281699380560", "2264868936960", "18198009147600", "146142982814208", "1173123636533454", "9413509300965936", "75513633110271264", "605598295606296000", "4855626127979443908", "38924245740546950784" ]

Card matching: coefficients B[n,1] of t in the reduced hit polynomial A[n,n,n](t).

A000280

[ "0", "1", "1", "2", "3", "11", "38", "1369", "56241", "2565782650", "177895665388171", "16891164530321501264425013171", "5629840598310484749297545401724540333537382" ]

a(n) = a(n-1) + a(n-2)^3.

A000281

[ "1", "3", "57", "2763", "250737", "36581523", "7828053417", "2309644635483", "898621108880097", "445777636063460643", "274613643571568682777", "205676334188681975553003", "184053312545818735778213457", "193944394596325636374396208563" ]

Expansion of cos(x)/cos(2x).

A000282

[ "3", "70", "3783", "338475", "40565585", "6061961733", "1083852977811", "225615988054171", "53595807366038234", "14308700593468127485", "4241390625289880226714", "1382214286200071777573643", "491197439886557439295166226", "189044982636675290371386547592", "78334771617452038208125184627931", "34771576300926271400714044414858372" ]

Finite automata.

A000283

[ "0", "1", "1", "2", "5", "29", "866", "750797", "563696885165", "317754178345286893212434", "100967717855888389973004846476977145423449281581" ]

a(n) = a(n-1)^2 + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.

A000284

[ "0", "1", "1", "2", "9", "731", "390617900", "59601394712394173339000731", "211723599072542785377729319366442939995427829921816290889198752331804918235791" ]

a(n) = a(n-1)^3 + a(n-2) with a(0)=0, a(1)=1.

A000285

[ "1", "4", "5", "9", "14", "23", "37", "60", "97", "157", "254", "411", "665", "1076", "1741", "2817", "4558", "7375", "11933", "19308", "31241", "50549", "81790", "132339", "214129", "346468", "560597", "907065", "1467662", "2374727", "3842389", "6217116", "10059505", "16276621", "26336126", "42612747", "68948873", "111561620", "180510493", "292072113", "472582606" ]

a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.

A000286

[ "0", "1", "1", "4", "5", "11", "20", "36", "65", "119", "218", "412", "770", "1466", "2784", "5322", "10226", "19691", "38048", "73665", "142927", "277822", "540851", "1054502", "2058507", "4023164", "7871226", "15414517", "30213010", "59266164", "116343183", "228545303", "449240025", "883569304", "1738768584", "3423466797", "6743729031" ]

Number of positive integers <= 2^n of form 2 x^2 + 5 y^2.

A000287

[ "1", "0", "4", "6", "24", "66", "214", "676", "2209", "7296", "24460", "82926", "284068", "981882", "3421318", "12007554", "42416488", "150718770", "538421590", "1932856590", "6969847486", "25237057110", "91729488354", "334589415276", "1224445617889", "4494622119424" ]

Number of rooted polyhedral graphs with n edges.

A000288

[ "1", "1", "1", "1", "4", "7", "13", "25", "49", "94", "181", "349", "673", "1297", "2500", "4819", "9289", "17905", "34513", "66526", "128233", "247177", "476449", "918385", "1770244", "3412255", "6577333", "12678217", "24438049", "47105854", "90799453", "175021573", "337364929", "650291809", "1253477764" ]

Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.

A000289

[ "1", "4", "7", "31", "871", "756031", "571580604871", "326704387862983487112031", "106735757048926752040856495274871386126283608871", "11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031" ]

A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).

A000290

[ "0", "1", "4", "9", "16", "25", "36", "49", "64", "81", "100", "121", "144", "169", "196", "225", "256", "289", "324", "361", "400", "441", "484", "529", "576", "625", "676", "729", "784", "841", "900", "961", "1024", "1089", "1156", "1225", "1296", "1369", "1444", "1521", "1600", "1681", "1764", "1849", "1936", "2025", "2116", "2209", "2304", "2401", "2500" ]

The squares: a(n) = n^2.

A000291

[ "2", "4", "9", "16", "29", "47", "77", "118", "181", "267", "392", "560", "797", "1111", "1541", "2106", "2863", "3846", "5142", "6808", "8973", "11733", "15275", "19753", "25443", "32582", "41569", "52770", "66757", "84078", "105555", "131995", "164566", "204450", "253292", "312799", "385285", "473183", "579722", "708353", "863553" ]

Number of bipartite partitions of n white objects and 2 black ones.

A000292

[ "0", "1", "4", "10", "20", "35", "56", "84", "120", "165", "220", "286", "364", "455", "560", "680", "816", "969", "1140", "1330", "1540", "1771", "2024", "2300", "2600", "2925", "3276", "3654", "4060", "4495", "4960", "5456", "5984", "6545", "7140", "7770", "8436", "9139", "9880", "10660", "11480", "12341", "13244", "14190", "15180" ]

Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.

A000293

[ "1", "1", "4", "10", "26", "59", "140", "307", "684", "1464", "3122", "6500", "13426", "27248", "54804", "108802", "214071", "416849", "805124", "1541637", "2930329", "5528733", "10362312", "19295226", "35713454", "65715094", "120256653", "218893580", "396418699", "714399381", "1281403841", "2287986987", "4067428375", "7200210523", "12693890803", "22290727268", "38993410516", "67959010130", "118016656268", "204233654229", "352245710866", "605538866862", "1037668522922", "1772700955975", "3019333854177", "5127694484375", "8683676638832", "14665233966068", "24700752691832", "41495176877972", "69531305679518" ]

a(n) = number of solid (i.e., three-dimensional) partitions of n.

A000294

[ "1", "1", "4", "10", "26", "59", "141", "310", "692", "1483", "3162", "6583", "13602", "27613", "55579", "110445", "217554", "424148", "820294", "1572647", "2992892", "5652954", "10605608", "19765082", "36609945", "67405569", "123412204", "224728451", "407119735", "733878402", "1316631730", "2351322765", "4180714647", "7401898452", "13051476707", "22922301583", "40105025130", "69909106888", "121427077241", "210179991927", "362583131144" ]

Expansion of g.f. Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).

A000295

[ "0", "0", "1", "4", "11", "26", "57", "120", "247", "502", "1013", "2036", "4083", "8178", "16369", "32752", "65519", "131054", "262125", "524268", "1048555", "2097130", "4194281", "8388584", "16777191", "33554406", "67108837", "134217700", "268435427", "536870882", "1073741793", "2147483616", "4294967263", "8589934558" ]

Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018).

A000296

[ "1", "0", "1", "1", "4", "11", "41", "162", "715", "3425", "17722", "98253", "580317", "3633280", "24011157", "166888165", "1216070380", "9264071767", "73600798037", "608476008122", "5224266196935", "46499892038437", "428369924118314", "4078345814329009", "40073660040755337", "405885209254049952", "4232705122975949401" ]

Set partitions without singletons: number of partitions of an n-set into blocks of size > 1. Also number of cyclically spaced (or feasible) partitions.

A000297

[ "0", "4", "12", "25", "44", "70", "104", "147", "200", "264", "340", "429", "532", "650", "784", "935", "1104", "1292", "1500", "1729", "1980", "2254", "2552", "2875", "3224", "3600", "4004", "4437", "4900", "5394", "5920", "6479", "7072", "7700", "8364", "9065", "9804", "10582", "11400", "12259", "13160", "14104", "15092", "16125", "17204" ]

a(n) = (n+1)*(n+3)*(n+8)/6.

A000298

[ "1", "4", "12", "30", "70", "159", "339", "706", "1436", "2853", "5551", "10622", "19975", "37043", "67811", "122561", "219090", "387578", "678977", "1178769", "2029115", "3465056", "5872648", "9882301", "16517284", "27430358", "45275673", "74297072", "121245153", "196810381", "317850809", "510830685", "817139589", "1301251186", "2063204707", "3257690903", "5123047561" ]

Number of partitions into non-integral powers.

A000299

[ "0", "0", "0", "0", "1", "4", "13", "36", "93", "225", "528", "1198", "2666", "5815", "12517", "26587", "55933", "116564", "241151", "495417", "1011950", "2055892", "4157514", "8371318", "16792066", "33564256", "66875221", "132849983", "263192599", "520087551", "1025295487", "2016745784", "3958608430", "7754810743" ]

Number of n-node rooted trees of height 4.

A000300

[ "1", "4", "14", "44", "133", "388", "1116", "3168", "8938", "25100", "70334", "196824", "550656", "1540832", "4314190", "12089368", "33911543", "95228760", "267727154", "753579420", "2123637318", "5991571428", "16923929406", "47857425416", "135478757308", "383929643780", "1089118243128", "3092612497260" ]

4th power of rooted tree enumerator: linear forests of 4 rooted trees.