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A036075 The number of partitions of {1..5n} that are invariant under a permutation consisting of n 5-cycles. 6
1, 2, 10, 70, 602, 6078, 70402, 917830, 13253002, 209350350, 3584098770, 66012131222, 1300004931162, 27232369503902, 604103160535330, 14136908333006822, 347827448896896554, 8971450949011952494 (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=5.

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, 5], {n, 0, 12}] (* Wouter Meeussen, Dec 06 2008 *)

mx = 16; p = 5; 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 Bell numbers; j=2, A002872; j=3, A002874; j=4, A141003 (Mathar); j=5, this sequence; j=6, A141004 (Mathar); j=7, A036077. - Wouter Meeussen, Dec 06 2008

Column 5 of A162663.

Sequence in context: A217938 A051405 A005568 * A212914 A123881 A289680

Adjacent sequences:  A036072 A036073 A036074 * A036076 A036077 A036078

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.)