A286072 Number of permutations of [n] where adjacent cycles differ in size.

1, 1, 1, 5, 16, 84, 512, 3572, 28080, 256820, 2553728, 28064776, 337319944, 4385615904, 61255920936, 921584068648, 14720437293952, 250190161426720, 4507229152534944, 85630125536152160, 1711040906290680448, 35969941361999955392, 790961860293623563648

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. A275313, A286071, A286073, A286074, A286075, A286076, A286077.

Programs

Maple

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

Mathematica

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