A332859 Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 56, 1992, 58566, 1569387, 40210458, 1011778943, 25407870031, 643294838111, 16530707226038, 433032539982493, 11597633757170403, 318186179384754262, 8953723541105483282, 258628065642282683675, 7671629851218367059371, 233734404206144319940526

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-François 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