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

0,4

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

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 *)

Crossrefs

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

Sequence in context: A123981 A123985 A219953 * A089066 A099030 A264657

Adjacent sequences: A286072 A286073 A286074 * A286076 A286077 A286078

Keyword

nonn

Author

Alois P. Heinz, May 01 2017

Status

approved