A364406 Number of permutations of [n] such that the minimal element of each cycle is also its length.

1, 1, 0, 1, 0, 0, 6, 6, 0, 0, 720, 2160, 9360, 19440, 30240, 3659040, 21772800, 228614400, 1632960000, 11125900800, 73025971200, 1708337433600, 15442053580800, 254260755302400, 3318429200486400, 46929444097536000, 546974781889536000, 7312714579602432000

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..474

Wikipedia, Permutation

Example

a(0) = 1: () the empty permutation.
a(1) = 1: (1).
a(3) = 1: (1)(23).
a(6) = 6: (1)(24)(356), (1)(24)(365), (1)(25)(346), (1)(25)(364),
  (1)(26)(345), (1)(26)(354).
a(7) = 6: (1)(23)(4567), (1)(23)(4576), (1)(23)(4657), (1)(23)(4675),
  (1)(23)(4756), (1)(23)(4765).

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
      b(n, i-1)+`if`(2*i>n+1, 0, b(n-i, i-1)*binomial(n-i, i-1)*(i-1)!)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..33);

Mathematica

b[n_, i_] := b[n, i] = If[i*(i + 1)/2 < n, 0, If[n == 0, 1, b[n, i - 1] + If[2*i > n + 1, 0, b[n - i, i - 1]*Binomial[n - i, i - 1]*(i - 1)!]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Dec 05 2023, after Alois P. Heinz *)

Crossrefs

Cf. A000142, A007837, A188431, A362362, A364207, A364277 A364279 A364281 A364283.

Sequence in context: A334710 A283203 A155742 * A005597 A281056 A273989

Adjacent sequences: A364403 A364404 A364405 * A364407 A364408 A364409

Keyword

nonn

Author

Alois P. Heinz, Jul 22 2023

Status

approved