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

9,2

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

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 *)

Crossrefs

Column k=9 of A322384.

Sequence in context: A302767 A078195 A103725 * A264505 A308101 A291129

Adjacent sequences: A332855 A332856 A332857 * A332859 A332860 A332861

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2020

Status

approved