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A036077 The number of partitions of {1..7n} that are invariant under a permutation consisting of n 7-cycles. 6
1, 2, 12, 106, 1144, 14434, 209736, 3451290, 63194936, 1269555762, 27700698344, 651497885482, 16414347638936, 440651469115394, 12546081858835528, 377328994871025210, 11946046637611280120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Original name: Sorting numbers.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]

OEIS Wiki, Sorting numbers

Index entries for sequences related to sorting

FORMULA

E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=7.

MATHEMATICA

u[0, j_]:=1; u[k_, j_]:=u[k, j]=Sum[Binomial[k-1, i-1]Plus@@(u[k-i, j]#^(i-1)&/@Divisors[j]), {i, k}]; Table[u[n, 7], {n, 0, 12}] (* Wouter Meeussen, Dec 06 2008 *)

mx = 16; p = 7; Range[0, mx]! CoefficientList[ Series[ Exp[ (Exp[p*x] - p - 1)/p + Exp[x]], {x, 0, mx}], x] (* Robert G. Wilson v, Dec 12 2012 *)

CROSSREFS

Cf. A001861, A002872-A002875, A036074.

u[n,j] generates for j=1, A000110; j=2, A002872; j=3, A002874; j=4, A141003; j=5, A036075; j=6, A141004; j=7, this sequence. - Wouter Meeussen, Dec 06 2008

Column 7 of A162663.

Sequence in context: A085867 A141133 A217801 * A275765 A184975 A268538

Adjacent sequences:  A036074 A036075 A036076 * A036078 A036079 A036080

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

New name from Danny Rorabaugh, Oct 24 2015

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)