A332858 Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 46, 1376, 34662, 808029, 18239040, 408622073, 9219406943, 211361047584, 4951434599465, 118953031062221, 2937244849150543, 74649387584172199, 1954230833420758243, 52717076107348326739, 1465510610406405412331, 41979421676766533788251, 1238736596075658751908901

Offset: 9

Author

Alois P. Heinz, Feb 26 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=9 of A322384.

Programs

Maple

b:= proc(n, l) option remember; `if`(n=0, l[9], add((j-1)!*b(n-j,
      sort([l[], j], `>`)[1..9])*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n, [0$9]):
seq(a(n), n=9..26);

Mathematica

b[n_, l_] := b[n, l] = If[n == 0, l[[9]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 9]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, Table[0, {9}]];
a /@ Range[9, 26] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)