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

0,4

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, 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 *)

Crossrefs

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

Sequence in context: A179683 A179685 A286077 * A002830 A365654 A370096

Adjacent sequences: A286069 A286070 A286071 * A286073 A286074 A286075

Keyword

nonn

Author

Alois P. Heinz, May 01 2017

Status

approved