This site is supported by donations to The OEIS Foundation.

User:Olivier Gérard/Permutations

From OeisWiki
Jump to: navigation, search

Study of all 2D sequences summing to a sequence related to permutations = n!

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 Sequences Partition sum = n!
A145271 1, 2, 6, 24, 120
A036039 1, 2, 6, 24, 120, 720, 5040
A102189 1, 2, 6, 24, 120, 720, 5040
A136100 1, 2, 6, 24, 120, 720, 5040
A181897 1, 2, 6, 24, 120, 720, 5040
OEIS Sequences Partition sum = n!/2
A178883 1, 3, 12, 60, 360, 2520, 20160
A212358 1, 1, 3, 12, 60, 360, 2520, 20160
Retrieved from "https://oeis.org/w/index.php?title=User:Olivier_Gérard/Permutations&oldid=1569257"