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A246050 Number of endofunctions on [2n] where the smallest cycle length equals n. 4
1, 3, 51, 4360, 861420, 302472576, 165549605760, 130241382036480, 139296260790086400, 194427690066299289600, 343266609438110040883200, 747889929370001008617062400, 1971026055567996899374212710400, 6180432763819774878006029844480000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 20:13 EST 2021. Contains 349585 sequences. (Running on oeis4.)