A246616 Number of endofunctions on [n] whose cycle lengths are multiples of 9.

1, 0, 0, 0, 0, 0, 0, 0, 0, 40320, 3628800, 219542400, 11496038400, 570031862400, 27908676956160, 1379187810000000, 69648048665395200, 3619848890071814400, 194428045753727385600, 10817313676715756770560, 624148118196535296000000, 37365232440634029661766400

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

E.g.f.: 1/(1+LambertW(-x)^9)^(1/9). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-4/9) * 2^(4/9) * sqrt(Pi) / (3^(2/9) * GAMMA(1/18)) * (1 - 52 * sqrt(2/n) * GAMMA(1/18) / (243 * GAMMA(5/9))). - Vaclav Kotesovec, Sep 01 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i>n, 0, add(b(n-i*j, i+9)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 9)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1+LambertW[-x]^9)^(1/9), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Crossrefs

Column k=9 of A246609.

Sequence in context: A213878 A179063 A246196 * A291115 A246219 A045516

Adjacent sequences: A246613 A246614 A246615 * A246617 A246618 A246619

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved