A246050 Number of endofunctions on [2n] where the smallest cycle length equals n.

1, 3, 51, 4360, 861420, 302472576, 165549605760, 130241382036480, 139296260790086400, 194427690066299289600, 343266609438110040883200, 747889929370001008617062400, 1971026055567996899374212710400, 6180432763819774878006029844480000

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..190

Formula

a(n) = A246049(2n,n) = A243098(2n,n).

a(n) ~ 2^(3*n-1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Aug 19 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i+1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> `if`(n=0, 1, A(2*n, n) -A(2*n, n+1)):
seq(a(n), n=0..15);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i>n, 0, Sum[(i-1)!^j*multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i+1], {j, 0, n/i}]]]; A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, k], {j, 0, n}]; a[n_] := If[n == 0, 1, A[2*n, n] - A[2*n, n+1]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 11 2015, after Alois P. Heinz *)

Crossrefs

Cf. A241982, A246049, A243098.

Sequence in context: A069343 A084882 A275798 * A091502 A307022 A330302

Adjacent sequences: A246047 A246048 A246049 * A246051 A246052 A246053

Keyword

nonn

Author

Alois P. Heinz, Aug 11 2014

Status

approved