A246615 Number of endofunctions on [n] whose cycle lengths are multiples of 8.

1, 0, 0, 0, 0, 0, 0, 0, 5040, 362880, 18144000, 804988800, 34488115200, 1482082842240, 65120246231040, 2955402450000000, 139297568464454400, 6837892496270035200, 350034595015623598080, 18692451288585606954240, 1041114148173066240000000

Offset

0,9

Links

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

Formula

E.g.f.: 1/(1-LambertW(-x)^8)^(1/8). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-7/16) * 2^(1/16) * (sqrt(Pi) / Gamma(1/16)) * (1 - 161 * sqrt(2/n) * Gamma(1/16) / (768 * Gamma(9/16))). - 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+8)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 8)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1-LambertW[-x]^8)^(1/8), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Crossrefs

Column k=8 of A246609.

Sequence in context: A342075 A055362 A246195 * A291114 A246218 A178140

Adjacent sequences: A246612 A246613 A246614 * A246616 A246617 A246618

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved