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A246618 Number of endofunctions on [2n] whose cycle lengths are multiples of n. 2
1, 4, 57, 4480, 866460, 302835456, 165589522560, 130247609057280, 139297568464454400, 194428045753727385600, 343266731083210449715200, 747889980460943180326502400, 1971026081420013638259189350400, 6180432779330984921337015828480000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..195

FORMULA

a(n) = A246609(2n,n).

a(n) ~ 2^(3*n-1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Sep 01 2014

MAPLE

with(combinat):

b:= proc(n, i, k) option remember; `if`(n=0, 1,

      `if`(i=0 or i>n, 0, add(b(n-i*j, i+k, k)*(i-1)!^j*

      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))

    end:

a:= n->add(b(j, n$2)*(2*n)^(2*n-j)*binomial(2*n-1, j-1), j=0..2*n):

seq(a(n), n=0..15);

MATHEMATICA

multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0 || i > n, 0, Sum[b[n - i*j, i + k, k]*(i - 1)!^j * multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!, {j, 0, n/i}]]]; a[0] = 1; a[n_] := Sum[b[j, n, n]*(2n)^(2n-j)*Binomial[2n-1, j-1], {j, 0, 2n}]; Table[a[n], {n, 0, 15}] (* Jean-Fran├žois Alcover, Feb 26 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A246609.

Sequence in context: A209316 A221866 A270881 * A103907 A108148 A099348

Adjacent sequences:  A246615 A246616 A246617 * A246619 A246620 A246621

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2014

STATUS

approved

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Last modified August 15 13:11 EDT 2020. Contains 336504 sequences. (Running on oeis4.)