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A332859 Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by decreasing lengths. 2
1, 56, 1992, 58566, 1569387, 40210458, 1011778943, 25407870031, 643294838111, 16530707226038, 433032539982493, 11597633757170403, 318186179384754262, 8953723541105483282, 258628065642282683675, 7671629851218367059371, 233734404206144319940526 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..450

Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.

Wikipedia, Permutation

MAPLE

b:= proc(n, l) option remember; `if`(n=0, l[10], add((j-1)!*b(n-j,

      sort([l[], j], `>`)[1..10])*binomial(n-1, j-1), j=1..n))

    end:

a:= n-> b(n, [0$10]):

seq(a(n), n=10..27);

MATHEMATICA

b[n_, l_] := b[n, l] = If[n == 0, l[[10]], Sum[(j-1)!*b[n-j, ReverseSort[ Append[l, j]][[1 ;; 10]]] Binomial[n - 1, j - 1], {j, 1, n}]];

a[n_] := b[n, Table[0, {10}]];

a /@ Range[10, 27] (* Jean-Fran├žois Alcover, Mar 01 2020, after Alois P. Heinz *)

CROSSREFS

Column k=10 of A322384.

Sequence in context: A038649 A004375 A103726 * A004387 A111597 A111781

Adjacent sequences:  A332856 A332857 A332858 * A332860 A332861 A332862

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 26 2020

STATUS

approved

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Last modified May 22 09:50 EDT 2022. Contains 353949 sequences. (Running on oeis4.)