A286074 Number of permutations of [n] with nondecreasing cycle sizes.

1, 1, 2, 4, 13, 45, 250, 1342, 10085, 76165, 715588, 6786108, 78636601, 896672473, 12112535378, 163963519810, 2534311844905, 39211836764457, 688584972407680, 12003902219337760, 234324625117308533, 4571805253649981173, 98183221386947058286

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.

a(n) mod 2 = A133872(n).

Links

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

Crossrefs

Cf. A133872, A275311, A286071, A286072, A286073, A286075, A286076, A286077.

Programs

Maple

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

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[(j - 1)!*b[n - j, j]*Binomial[n - 1, j - 1], {j, i, n}]];
a[n_] := b[n, 1];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 25 2018, translated from Maple *)