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A246615 Number of endofunctions on [n] whose cycle lengths are multiples of 8. 2
1, 0, 0, 0, 0, 0, 0, 0, 5040, 362880, 18144000, 804988800, 34488115200, 1482082842240, 65120246231040, 2955402450000000, 139297568464454400, 6837892496270035200, 350034595015623598080, 18692451288585606954240, 1041114148173066240000000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 06:18 EST 2022. Contains 350601 sequences. (Running on oeis4.)