A286075 Number of permutations of [n] with increasing cycle sizes.

1, 1, 1, 3, 8, 38, 182, 1194, 7932, 69192, 591936, 6286272, 66914880, 840036960, 10567285920, 154755036000, 2246755924800, 37283584936320, 618705247829760, 11472473012232960, 212762383625594880, 4386435706887413760, 89954629722500659200, 2030764767987849062400

Offset: 0

Author

Alois P. Heinz, May 01 2017

Keywords

• nonn

Comments

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450
• Wikipedia, Permutation

Crossrefs

Cf. A275312, A286071, A286072, A286073, A286074, A286076, A286077.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
      b(n, i+1)+b(n-i, i+1)*(i-1)!*binomial(n-1, i-1)))
    end:
a:= n-> b(n, 1):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]*(i - 1)!*Binomial[n - 1, i - 1]]];
a[n_] := b[n, 1];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 28 2018, from Maple *)