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User:Olivier Gérard/Permutations
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Study of all 2D sequences summing to a sequence related to permutations = n!
Contents
Table of searched sums
Searched Sequence | Name or definition | Anum | Total | Tri | Shr | Alt | Lin | Bino | |
---|---|---|---|---|---|---|---|---|---|
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 | Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters). | A000142 | 204 | 146 | 30 | 47 | 16 | 13 | |
0, 0, 1, 5, 23, 119, 719, 5039, 40319, 362879 | n! - 1. | A033312 | 89 | 12 | 74 | 1 | 3 | 6 | |
1, 1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400 | Order of alternating group A_n, or number of even permutations of n letters. | A001710 | 49 | 22 | 12 | 4 | 12 | 3 | |
0, 1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920 | a(n) = n*n! = (n+1)! - n!. | A001563 | 34 | 6 | 20 | 0 | 8 | 2 | |
1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075 | Double factorial of odd numbers: (2*n-1)!! = 1*3*5*...*(2*n-1). | A001147 | 30 | 20 | 5 | 7 | 4 | 3 | |
1, 3, 9, 28, 90, 297, 1001, 3432, 11934, 41990 | 3*(2*n)!/((n+2)!*(n-1)!). | A000245 | 24 | 6 | 13 | 5 | 5 | 0 | |
1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496 | Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points. | A000166 | 22 | 3 | 6 | 4 | 6 | 4 | |
1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560 | Double factorial of even numbers: (2n)!! = 2^n*n!. | A000165 | 21 | 18 | 0 | 2 | 5 | 2 | |
0, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576 | Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1)=(n+1)*a(n)+n!. | A000254 | 18 | 7 | 3 | 0 | 9 | 4 | |
1, 2, 12, 120, 1680, 30240, 665280, 17297280, 518918400 | Quadruple factorial numbers: (2*n)!/n!. | A001813 | 17 | 8 | 0 | 5 | 1 | 3 | |
1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936 | Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also number of alternating permutations on n letters. | A000111 | 16 | 14 | 3 | 6 | 1 | 0 | |
0, 1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600 | Lah numbers: (n-1)*n!/2. | A001286 | 15 | 3 | 9 | 1 | 3 | 1 | |
0, 1, 1, 2, 4, 10, 26, 76, 232, 764 | Number of self-inverse permutations on n letters, also known as involutions; number of Young tableaux with n cells. | A000085 | 14 | 13 | 2 | 4 | 3 | 1 | |
0, 1, 1, 4, 15, 76, 455, 3186, 25487, 229384 | The game of Mousetrap with n cards (given n letters and n envelopes, how many ways are there to fill the envelopes so that at least one letter goes into its right envelope?). | A002467 | 14 | 4 | 5 | 2 | 4 | 1 | |
1, 1, 4, 15, 64, 325, 1956, 13699, 109600, 986409 | a(n) = n(a(n-1) + 1). | A007526 | 14 | 1 | 7 | 0 | 4 | 3 | |
1, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760 | a(0) = 0; a(n+1) = 2*n! (n >= 0). | A052849 | 14 | 7 | 2 | 1 | 4 | 2 | |
0, 1, 5, 26, 154, 1044, 8028, 69264, 663696, 6999840 | Generalized Stirling numbers: a(n) = n!*Sum[(k+1)/(n-k),k,0,n-1]. | A001705 | 13 | 1 | 6 | 1 | 8 | 3 | |
1, 4, 20, 120, 840, 6720, 60480, 604800, 6652800, 79833600 | n!/6. | A001715 | 13 | 5 | 3 | 1 | 4 | 0 | |
1, 2, 5, 16, 65, 326, 1957, 13700, 109601, 986410 | Total number of arrangements of a set with n elements: a(n) = Sum_k=0..n n!/k!. | A000522 | 12 | 8 | 0 | 2 | 2 | 1 | |
0, 2, 11, 35, 85, 175, 322, 546, 870, 1320 | Stirling numbers of first kind: s(n+2,n). | A000914 | 11 | 4 | 4 | 0 | 3 | 0 | |
0, 1, 3, 10, 41, 206, 1237, 8660, 69281, 623530 | a(n) = n*a(n-1) + 1, a(0) = 0. | A002627 | 11 | 6 | 2 | 0 | 2 | 1 | |
1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600 | a(0) = 1; for n>0, a(n) = 2^(n-1)*n!. | A002866 | 11 | 9 | 1 | 0 | 0 | 2 | |
0, 2, 12, 72, 480, 3600, 30240, 282240, 2903040, 32659200 | n! * (n-1). | A062119 | 11 | 0 | 5 | 1 | 5 | 0 | |
1, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680 | n! + (n-1)!. | A001048 | 10 | 1 | 0 | 0 | 8 | 2 | |
2, 8, 40, 240, 1680, 13440, 120960, 1209600, 13305600, 159667200 | n!/3. | A002301 | 9 | 2 | 3 | 1 | 3 | 0 | |
0, 0, 2, 9, 40, 205, 1236, 8659, 69280, 623529 | n! * sum(k=1..n-1, 1/k! ). | A038156 | 9 | 1 | 7 | 0 | 1 | 1 | |
0, 1, 0, 3, 8, 45, 264, 1855, 14832, 133497 | Rencontres numbers: permutations with exactly one fixed point. | A000240 | 8 | 0 | 0 | 1 | 3 | 4 | |
1, 3, 10, 42, 216, 1320, 9360, 75600, 685440, 6894720 | (2n+1)*n!. | A007680 | 8 | 1 | 1 | 1 | 5 | 0 | |
0, 0, 1, 4, 17, 86, 517, 3620, 28961, 260650 | a(n) = n*a(n-1) + 1, a(1) = 0. | A056542 | 8 | 1 | 4 | 0 | 2 | 1 | |
1, 5, 22, 114, 696, 4920, 39600, 357840, 3588480, 39553920 | Table[i! - (i - 2)!, i, 2, 16] | FactPot_5 | 7 | 0 | 5 | 0 | 1 | 1 | |
1, 1, 5, 61, 1385, 50521, 2702765, 199360981 | Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sech(x)=1/cosh(x). | A000364 | 6 | 6 | 3 | 0 | 0 | 0 | |
1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200 | n!/24. | A001720 | 5 | 3 | 1 | 1 | 0 | 0 | |
1, 0, 1, 1, 5, 19, 101, 619, 4421, 35899 | Alternating factorials: n! - (n-1)! + (n-2)! - ... 1!. | A005165 | 5 | 0 | 1 | 2 | 1 | 1 | |
0, 1, 5, 26, 157, 1100, 8801, 79210, 792101, 8713112 | Table[X000010[i], i, 0, 14] | FactPot_69 | 5 | 0 | 5 | 0 | 0 | 0 | |
1, 1, 4, 36, 576, 14400, 518400, 25401600, 1625702400 | (n!)^2. | A001044 | 4 | 3 | 0 | 0 | 0 | 1 | |
1, 2, 16, 272, 7936, 353792, 22368256, 1903757312 | Tangent (or "Zag") numbers: expansion of tan(x), also expansion of tanh(x). | A000182 | 3 | 2 | 0 | 1 | 1 | 0 | |
2, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680 | n! + (n-1)!. | A001048 | 3 | 0 | 0 | 0 | 2 | 2 | |
1, 2, 4, 9, 28, 125, 726, 5047, 40328, 362889 | n! + n. | A005095 | 3 | 3 | 0 | 0 | 0 | 0 | |
1, 2, 12, 144, 2880, 86400, 3628800, 203212800 | n!*(n+1)!. | A010790 | 3 | 1 | 0 | 2 | 0 | 0 | |
0, 0, 4, 33, 236, 1795, 15114, 141113, 1451512, 16329591 | Table[i!/2 + 2 - i - (i - 1)!, i, 2, 16] | FactPot_10 | 3 | 1 | 1 | 0 | 1 | 0 | |
1, 0, 2, 3, 16, 75, 456, 3185, 25488, 229383 | Table[i! - Subfactorial[i] + (-1)^i, i, 0, 14] | FactPot_40 | 3 | 0 | 1 | 1 | 0 | 1 | |
0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576 | Unsigned Stirling numbers of first kind s(n,3). | A000399 | 2 | 2 | 1 | 0 | 0 | 0 | |
1, 2, 24, 720, 40320, 3628800, 479001600 | (2n)!. | A010050 | 2 | 2 | 0 | 0 | 0 | 0 | |
0, 1, 3, 8, 27, 124, 725, 5046, 40327, 362888 | (n+1)!+ n. | A030495 | 2 | 0 | 1 | 0 | 1 | 0 | |
0, 1, 0, 2, 4, 20, 100, 620, 4420, 35900 | Alternating factorials: 0! - 1! + 2! - ... + (-1)^n n! | A058006 | 2 | 0 | 0 | 1 | 0 | 1 | |
1, 2, 7, 30, 156, 960, 6840, 55440, 504000, 5080320 | a(0) = 1; for n > 0, a(n) = (n!*(3*n+1))/2. | A066114 | 2 | 0 | 0 | 0 | 2 | 0 | |
2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760 | Product of factorials of the digits of n. | A066459 | 2 | 0 | 0 | 0 | 0 | 2 | |
1, 2, 3, 12, 60, 360, 2520, 20160, 181440, 1814400 | Row sums of 1-Euler triangle A188587. | A188588 | 2 | 2 | 0 | 0 | 0 | 0 | |
1, 1, 2, 3, 8, 15, 48, 105, 384, 945 | Double factorials n!!: a(n)=n*a(n-2), a(0)=a(1)=1. | A006882 | 1 | 0 | 0 | 0 | 1 | 0 | |
2, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600 | Number of reversible strings with n labeled beads of 2 colors. | A032107 | 1 | 1 | 0 | 0 | 0 | 0 | |
2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881 | n! + 1. | A038507 | 1 | 0 | 1 | 0 | 0 | 0 | |
0, 6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200 | E.g.f. x^3/(1-x)^2. | A052571 | 1 | 0 | 1 | 0 | 0 | 0 | |
2, 6, 30, 216, 2040, 23760, 327600, 5201280, 93260160, 1861574400 | E.g.f. (2-4x+x^2)/((1-x)(1-2x)). | A052584 | 1 | 1 | 0 | 0 | 0 | 0 | |
0, 1, 1, 4, 8, 28, 76, 272, 880, 3328 | A recurrence equation. | A059480 | 1 | 1 | 0 | 1 | 0 | 0 | |
4, 15, 72, 420, 2880, 22680, 201600, 1995840, 21772800, 259459200 | (n+1)*(n-1)!/2. | A171005 | 1 | 0 | 0 | 0 | 0 | 1 | |
1, 2, 9, 124, 2765, 85686, 3623767, 203172488 | Table[i*((i - 1)!*((i - 1)! - 1) + 1), i, 1, 15] | FactPot_34 | 1 | 1 | 0 | 0 | 0 | 0 | |
2, 1, 2, 2, 6, 20, 102, 620, 4422, 35900 | Table[FactBS[i] + 1, i, 0, 14] | FactPot_36 | 1 | 0 | 0 | 1 | 0 | 0 | |
0, 0, 1, 4, 19, 100, 619, 4420, 35899, 326980 | Table[i! - FactBS[i] - (1 + (-1)^(1 + i))/2, i, 0, 14] | FactPot_38 | 1 | 0 | 0 | 1 | 0 | 0 | |
1, 2, 5, 28, 269, 3126, 41047, 604808, 9959049, 182165770 | Table[(2*i)!! + 1 + i - (i + 1)!, i, 0, 14] | FactPot_41 | 1 | 1 | 0 | 0 | 0 | 0 | |
1, 2, 11, 68, 499, 4554, 51113, 685432, 10684791, 189423350 | Table[(2*i)!! - 1 - i + (i + 1)!, i, 0, 14] | FactPot_42 | 1 | 1 | 0 | 0 | 0 | 0 | |
1, 0, 5, 17, 97, 599, 4321, 35279, 322561, 3265919 | Table[(i + 1)! - i! + (-1)^i, i, 0, 14] | FactPot_43 | 1 | 0 | 0 | 1 | 0 | 0 | |
0, 1, 10, 138, 2856, 86280, 3628080, 203207760 | Table[i!*(i - 1)! - (i - 1)!, i, 1, 15] | FactPot_44 | 1 | 0 | 0 | 1 | 0 | 0 | |
0, 0, 1, 2, 7, 18, 61, 188, 677, 2370 | Table[X000012[i], i, 0, 14] | FactPot_71 | 1 | 0 | 1 | 0 | 0 | 0 | |
0, 0, 1, 2, 6, 15, 46, 137, 460, 1557 | Table[X000014[i], i, 0, 14] | FactPot_74 | 1 | 0 | 1 | 0 | 0 | 0 | |
0, 0, 1, 2, 5, 12, 33, 94, 293, 952 | Table[X000015[i], i, 0, 14] | FactPot_76 | 1 | 0 | 1 | 0 | 0 | 0 | |
0, 6, 50, 225, 735, 1960, 4536, 9450, 18150, 32670 | Stirling numbers of first kind, s(n+3,n), negated. | A001303 | 0 | 0 | 0 | 0 | 0 | 0 | |
1, 6, 120, 5040, 362880, 39916800, 6227020800 | (2*n+1)!. | A009445 | 0 | 0 | 0 | 0 | 0 | 0 | |
2, 3, 7, 22, 89, 446, 2677, 18740, 149921, 1349290 | a(n) = n*a(n-1) + 1, a(0) = 2. | A038159 | 0 | 0 | 0 | 0 | 0 | 0 | |
1, 6, 360, 60480, 19958400 | (3n)!/n!. | A064350 | 0 | 0 | 0 | 0 | 0 | 0 | |
2, 6, 48, 720, 17280, 604800, 29030400, 1828915200 | Second column (m=1) sequence of triangle A129462 (v=2 member of a certain family). | A129464 | 0 | 0 | 0 | 0 | 0 | 0 | |
1, 1, 9, 265, 14833, 1334961, 176214841 | Table[Subfactorial[2*i], i, 0, 14] | FactPot_14 | 0 | 0 | 0 | 0 | 0 | 0 | |
0, 2, 44, 1854, 133496, 14684570, 2290792932 | Table[Subfactorial[2*i + 1], i, 0, 14] | FactPot_15 | 0 | 0 | 0 | 0 | 0 | 0 | |
2, 3, 5, 10, 29, 126, 727, 5048, 40329, 362890 | Table[i! + i + 1, i, 0, 14] | FactPot_25 | 0 | 0 | 0 | 0 | 0 | 0 | |
2, 1, 2, 9, 44, 235, 1434, 10073, 80632, 725751 | Table[2*i! - i, i, 0, 14] | FactPot_3 | 0 | 0 | 0 | 0 | 0 | 0 | |
1, 6, 180, 10080, 831600, 90810720 | Table[(3*i)!/i!^2, i, 0, 14] | FactPot_55 | 0 | 0 | 0 | 0 | 0 | 0 | |
2, 7, 29, 146, 877, 6140, 49121, 442090, 4420901, 48629912 | Table[X000011[i], i, 0, 14] | FactPot_70 | 0 | 0 | 0 | 0 | 0 | 0 | |
0, 0, 1, 2, 8, 21, 78, 247, 950, 3421 | Table[X000013[i], i, 0, 14] | FactPot_72 | 0 | 0 | 0 | 0 | 0 | 0 | |
0, 0, 1, 2, 9, 24, 97, 314, 1285, 4740 | Table[X000016[i], i, 0, 14] | FactPot_78 | 0 | 0 | 0 | 0 | 0 | 0 |
Table of all triangular sequences
OEIS Sequences | Triangular sum = n! |
---|---|
A126440 | 1, 2, 6, 24, 120, 720 |
A134832 | 1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320 |
A140711 | 1, 2, 6, 24, 120 |
A164652 | 0, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 |
A062867 | 1, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 |
A010026, A047921, A059427, A064482, A064484, A120434, A125553, A138770, A152874, A153592, A155755, A180887 | 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 |
A008290, A028305, A047919, A048994, A054654, A058057, A060338, A060523, A060524, A071818, A079642, A080018, A080061, A085771, A094314, A094315, A097591, A097898, A098825, A121554, A121585, A121697, A121745, A122890, A123125, A132393, A132795, A134830, A136572, A145878, A145893, A145894, A156368, A158830, A173018, A180193, A180196, A184184, A186358, A186754, A186759, A186761, A187247, A195581, A200545, A202992 | 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 |
A001100, A008275, A008276, A008292, A008304, A010027, A047874, A047918, A054115, A056151, A059418, A059438, A064315, A092580, A092582, A092583, A092594, A092741, A094067, A094112, A094638, A094785, A100822, A109878, A115755, A116854, A121581, A121634, A121637, A121692, A121698, A121748, A123513, A125182, A125183, A126065, A126074, A130152, A130477, A130534, A132005, A134433, A134436, A136125, A136715, A136716, A136717, A137312, A137320, A138771, A140709, A141476, A144107, A145876, A145877, A145888, A147679, A152660, A152938, A152970, A154986, A162976, A164645, A167565, A177262, A177263, A177264, A179454, A180013, A180188, A180190, A184180, A184182, A186370, A191716, A191718, A208956, A211318 | 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800 |
OEIS Sequences | Triangular sum = n!/2 |
A128613 | 0, 1, 3, 12, 60, 360, 2520, 20160, 181440 |
A132178 | 0, 1, 1, 1, 3, 12, 60, 360, 2520, 20160 |
A145224 | 1, 1, 1, 3, 12, 60, 360, 2520, 20160, 181440 |
A145225 | 0, 0, 1, 3, 12, 60, 360, 2520, 20160, 181440 |
A010028, A086856, A128612 | 1, 1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400 |
A008970, A049444, A065826, A122843, A136124, A137339, A143491, A144696, A145324, A159930, A162608, A168391, A179457 | 1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400 |
OEIS Sequences | Triangular sum = (n+1)!-n! |
A094485, A122844, A130493 | 1, 4, 18, 96, 600, 4320, 35280 |
OEIS Sequences | Triangular sum =n!-1 |
A008291, A125714 | 1, 5, 23, 119, 719, 5039, 40319, 362879, 3628799 |
OEIS Sequences | Triangular sum = n!+n |
A135723 | 1, 2, 4, 9, 28, 125, 726, 5047, 40328, 362889 |
OEIS Sequences | Triangular sum = binotrans((n+1)!)+1 |
A176663 | 1, 2, 2, 6, 20, 102, 620, 4422, 35900, 326982 |
OEIS Sequences | Shifted Triangular sum |
---|---|
A165325 | 6, 24, 120, 720, 5040 |
A152877 | 2, 6, 24, 120, 720, 5040, 40320 |
A178126 | 1, 6, 24, 120, 720, 5040, 40320, 362880 |
A121632 | 2, 6, 24, 120, 720, 5040, 40320, 362880 |
A145879 | 2, 6, 24, 120, 720, 5040, 40320, 362880 |
OEIS Sequences | Shifted Triangular sum = n!/2 |
A145225 | 0, 1, 3, 12, 60, 360, 2520, 20160, 181440 |
OEIS Sequences | Shifted Triangular sum = (n+1)!+n! |
A142156 | 1, 3, 8, 30, 144, 840, 5760 |
OEIS Sequences | Shifted Triangular sum = n!+1 |
A063851 | 1, 2, 3, 7, 25 |
Table of all alternating sign triangular sums
OEIS seq | Triangular sum | Sum Anum | Alternate sum | Alternate Anum |
---|---|---|---|---|
A105060 | 1, 6, 29, 148, 867, 5906, 46225 | ? | 1, 4, 19, 100, 619, 4420, 35899 | ? |
A119741 | 2, 9, 40, 205, 1236, 8659, 69280 | A038156 | 2, 3, 16, 75, 456, 3185, 25488 | ? |
A130478 | 1, 4, 11, 37, 163, 907, 6067 | A130494 | 1, 0, 5, 17, 97, 599, 4321 | ? |
A142148 | 1, 2, 9, 84, 1500, 43560, 1816920 | ? | 1, 0, 1, 10, 138, 2856, 86280 | ? |
A046803 | 1, 3, 10, 41, 206, 1237, 8660 | A002627 | 1, 1, 2, 5, 16, 61, 272 | A000111 |
A185421 | 1, 3, 14, 87, 676, 6303, 68564 | A185323 | 1, 1, 2, 5, 16, 61, 272 | A000111 |
A008826 | 1, 4, 32, 436, 9012, 262760, 10270696 | A005121 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A039814 | 1, 3, 14, 88, 694, 6578, 72792 | A007840 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A048159 | 1, 4, 32, 396, 6692, 143816, 3756104 | A005263 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A048160 | 1, 3, 22, 262, 4336, 91984, 2381408 | A005264 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A056856 | 1, 3, 20, 210, 3024, 55440, 1235520 | A006963 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A059604 | 1, 3, 20, 222, 3624, 80880, 2349360 | ? | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A073107 | 1, 3, 10, 38, 168, 872, 5296 | A010842 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A075513 | 1, 3, 18, 170, 2200, 36232, 725200 | A074932 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A079638 | 1, 4, 24, 192, 1920, 23040, 322560 | A002866 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A103718 | 1, 3, 10, 42, 216, 1320, 9360 | A007680 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A123670 | 1, 6, 60, 840, 15120, 332640, 8648640 | A000407 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A126671 | 0, 1, 4, 20, 128, 1024, 9984 | A126674 | 0, 1, 2, 6, 24, 120, 720 | A000142 |
A131222 | 1, 1, 4, 24, 192, 1920, 23040 | A002866 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A131758 | 1, 1, 4, 34, 368, 4416, 56352 | ? | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A134991 | 1, 4, 26, 236, 2752, 39208, 660032 | A000311 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A137394 | 1, 6, 30, 168, 1080, 7920, 65520 | A175925 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A142158 | 0, 2, 8, 110, 2112, 51984, 1560960 | ? | 0, 0, 2, 6, 24, 120, 720 | A000142 |
A154715 | 1, 5, 38, 406, 5672, 98424, 2046256 | ? | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A167568 | 1, 2, 10, 56, 456, 4368, 51792 | ? | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A168295 | 1, 3, 22, 258, 4104, 81960, 1966320 | ? | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A169593 | 1, 2, 3, 6, 26, 600, 195492 | ? | 1, 0, 1, 2, 6, 24, 120 | A000142 |
A199221 | 1, 1, 7, 38, 226, 1524, 11628 | ? | 1, 1, 1, 2, 6, 24, 120 | A000142 |
A028421, A136426 | 0, 1, 3, 11, 50, 274, 1764 | A000254 | 0, 1, 1, 1, 2, 6, 24 | A000142 |
A074246, A196837 | 1, 5, 26, 154, 1044, 8028, 69264 | A001705 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A049458, A143492, A196845 | 1, 4, 20, 120, 840, 6720, 60480 | A001715 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A008279 | 1, 2, 5, 16, 65, 326, 1957 | A000522 | 1, 0, 1, 2, 9, 44, 265 | A000166 |
A094587 | 1, 2, 5, 16, 65, 326, 1957 | A000522 | 1, 0, 1, 2, 9, 44, 265 | A000166 |
A158359 | 1, 2, 5, 16, 65, 326, 1957 | A000522 | 1, 0, 1, 0, 1, 2, 9 | A000166 |
A162995 | 1, 4, 17, 86, 517, 3620, 28961 | A056542 | 1, 2, 9, 44, 265, 1854, 14833 | A000166 |
A104033 | 1, 4, 36, 624, 18256, 814144, 51475776 | A002084 | 1, 2, 16, 272, 7936, 353792, 22368256 | A000182 |
A068424 | 1, 4, 15, 64, 325, 1956, 13699 | A007526 | 1, 0, 3, 8, 45, 264, 1855 | A000240 |
A042977 | 1, 3, 19, 185, 2437, 40523, 814355 | ? | 1, 1, 3, 15, 105, 945, 10395 | A001147 |
A123516 | 1, 3, 19, 189, 2601, 46035, 998955 | ? | 1, 1, 3, 15, 105, 945, 10395 | A001147 |
A176860 | 1, 10, 132, 2192, 44040, 1040112, 28254016 | ? | 1, 6, 36, 240, 1800, 15120, 141120 | A001286 |
A096747 | 1, 2, 5, 17, 74, 394, 2484 | A000774 | 1, 0, 1, 3, 12, 60, 360 | A001710 |
A109822 | 1, 3, 11, 50, 274, 1764, 13068 | A000254 | 1, 1, 3, 12, 60, 360, 2520 | A001710 |
A049459, A143493 | 1, 5, 30, 210, 1680, 15120, 151200 | A001720 | 1, 3, 12, 60, 360, 2520, 20160 | A001710 |
A173333, A181511 | 1, 3, 10, 41, 206, 1237, 8660 | A002627 | 1, 1, 4, 15, 76, 455, 3186 | A002467 |
A165680 | 1, 2, 3, 5, 11, 35, 155 | A067078 | 1, 0, 1, 1, 5, 19, 101 | A005165 |
A166350 | 1, 3, 9, 33, 153, 873, 5913 | A007489 | 1, 1, 5, 19, 101, 619, 4421 | A005165 |
A027858 | 1, 8, 108, 2304, 72000, 3110400, 177811200 | A084915 | 1, 2, 12, 144, 2880, 86400, 3628800 | A010790 |
A119502 | 1, 2, 4, 10, 34, 154, 874 | A003422 | 1, 0, 2, 4, 20, 100, 620 | A058006 |
Small candidates | ||||
A032355 | 1, 4, 10, 19, 42 | ? | 1, 0, 2, 3, 12 | A001390 |
A060040 | 1, 3, 6, 11, 19 | A001911 | 1, 1, 2, 3, 7 | A000057 |
A107499 | 1, 0, 2, 4, 24 | A001510 | 1, 0, 2, 4, 20 | A002558 |
Suplementary candidates | ||||
A198898 | 1, 2, 5, 6, 14 | A000092 | 1, 2, 1, 2, 2 | A000002 |
A027583 | 1, 2, 7, 18, 50 | A074141 | 1, 2, 3, 8, 30 | A001048 |
Shifted Alternating pairs
OEIS seq | Triangular sum | Sum Anum | Alternate sum | Alternate Anum |
---|---|---|---|---|
A178126 | 1, 6, 24, 120, 720, 5040, 40320 | A000142 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A181996 | 1, 4, 26, 236, 2752, 39208 | A000311 | 1, 2, 6, 24, 120, 720 | A000142 |
A204126 | 2, 5, 17, 74, 394, 2484, 18108 | A000774 | 0, 1, 1, 2, 6, 24, 120 | A000142 |
A144505 | 1, 3, 13, 77, 591, 5627, 64261 | A043301 | 1, 1, 3, 15, 105, 945, 10395 | A001147 |
A144944 | 1, 2, 7, 28, 121, 550 | A010683 | 1, 0, 1, 4, 15, 76 | A002467 |
A157047 | 1, 2, 4, 17, 123, 1197, 14233 | ? | 1, 0, 0, 1, 5, 23, 119 | A033312 |
Small candidates | ||||
A086389 | 1, 5, 8, 13, 23 | A009203 | 1, 1, 2, 3, 7 | A000057 |
A127311 | 1, 3, 10, 23, 51 | A080204 | 1, 1, 2, 3, 7 | A000057 |
A058301 | 0, 5, 10, 19, 112 | ? | 0, 1, 2, 3, 16 | A003963 |
A058730 | 1, 2, 4, 9, 26, 101 | A002773 | 1, 0, 2, 1, 2, 9 | A002079
|
Absolute / Alternating pairs
Self similar pairs Absolute/Alternating pairs
OEIS seq | Triangular sum | Sum Anum | Alternate sum | Alternate Anum |
---|---|---|---|---|
A147308, A147309, A147311, A147312 | 1, 1, 1, 2, 5, 16, 61 | A000111 | 1, 1, 1, 2, 5, 16, 61 | A000111 |
A060338, A060524, A097591, A136572, A145893, A145894, A164652, A180193, A191716, A191718 | 1, 2, 6, 24, 120, 720, 5040 | A000142 | 1, 2, 6, 24, 120, 720, 5040 | A000142 |
A076256, A076257 | 1, 2, 8, 48, 384, 3840, 46080 | A000165 | 1, 2, 8, 48, 384, 3840, 46080 | A000165 |
A161198 | 1, 3, 15, 105, 945, 10395, 135135 | A001147 | 1, 1, 1, 3, 15, 105, 945 | A001147 |
A039683, A161119 | 1, 1, 3, 15, 105, 945, 10395 | A001147 | 1, 1, 3, 15, 105, 945, 10395 | A001147 |
A137513 | 1, 2, 4, 12, 48, 240, 1440 | A052849 | 1, 2, 4, 12, 48, 240, 1440 | A052849 |
Changing Absolute/Alternating pairs
OEIS seq | Triangular sum | Sum Anum | Alternate sum | Alternate Anum |
---|---|---|---|---|
A049444, A136124, A143491, A145324, A168391 | 1, 3, 12, 60, 360, 2520, 20160 | A001710 | 1, 1, 2, 6, 24, 120, 720 | A000142 |
A087736 | 1, 1, 5, 61, 1385, 50521, 2702765 | A000364 | 1, 1, 3, 15, 105, 945, 10395 | A001147 |
A027477 | 1, 4, 36, 576, 14400, 518400, 25401600 | A001044 | 1, 2, 12, 144, 2880, 86400, 3628800 | A010790 |
A140709 | 1, 2, 6, 24, 120, 720, 5040 | A000142 | 1, 0, 2, 12, 72, 480, 3600 | A062119 |
Table of all partition like sequences
OEIS Sequence | Row Length | Row Order | Partition sum = n! |
---|---|---|---|
A145271 | A00041 | R A+S | 1, 2, 6, 24, 120 |
A036039 | A00041 | A+S | 1, 2, 6, 24, 120, 720, 5040 |
A102189 | A00041 | 1, 2, 6, 24, 120, 720, 5040 | |
A136100 | A00041 | 1, 2, 6, 24, 120, 720, 5040 | |
A181897 | A00041 | 1, 2, 6, 24, 120, 720, 5040 | |
OEIS Sequences | Row Length | Row Order | Partition sum = n!/2 |
A178883 | A00041 | 1, 3, 12, 60, 360, 2520, 20160 | |
A212358 | A00041 | 1, 1, 3, 12, 60, 360, 2520, 20160 |