A332853 Number of entries in the fourth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 11, 101, 932, 9185, 98317, 1141614, 14297174, 192303794, 2767778378, 42482344932, 692989979996, 11977186926515, 218693683265139, 4207257180352118, 85067513019575426, 1803695291827381964, 40022639769763695724, 927602835889551674104, 22416055484058795043176

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..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[4], add((j-1)!*b(n-j,
      sort([l[], j], `>`)[1..4])*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n, [0$4]):
seq(a(n), n=4..24);

Mathematica

b[n_, l_] := b[n, l] = If[n == 0, l[[4]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 4]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, {0, 0, 0, 0}];
a /@ Range[4, 24] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A322384.

Sequence in context: A138894 A287832 A122105 * A289850 A351811 A171750

Adjacent sequences: A332850 A332851 A332852 * A332854 A332855 A332856

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2020

Status

approved