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

Author

Alois P. Heinz, Feb 26 2020

Keywords

• nonn

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

Crossrefs

Column k=10 of A322384.

Programs

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 *)