A286073 Number of permutations of [n] with decreasing cycle sizes.

1, 1, 1, 4, 12, 60, 340, 2280, 17220, 151872, 1459584, 15624000, 182318400, 2316837600, 31596570720, 465582237120, 7283287851840, 121620647715840, 2149774858183680, 40196871701360640, 790002144844738560, 16364478334463078400, 354458730544573132800

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>i*(i+1)/2, 0, `if`(n=0, 1, b(n, i-1)+
      `if`(i>n, 0, b(n-i, i-1)*(i-1)!*binomial(n-1, i-1))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n > i*(i + 1)/2, 0, If[n == 0, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i - 1]*(i - 1)!*Binomial[n - 1, i - 1]]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 24 2018, translated from Maple *)

Crossrefs

Cf. A275309, A286071, A286072, A286074, A286075, A286076, A286077.

Sequence in context: A351286 A335656 A355268 * A357711 A337291 A324693

Adjacent sequences: A286070 A286071 A286072 * A286074 A286075 A286076

Keyword

nonn

Author

Alois P. Heinz, May 01 2017

Status

approved