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A246613 Number of endofunctions on [n] whose cycle lengths are multiples of 6. 2
1, 0, 0, 0, 0, 0, 120, 5040, 161280, 4898880, 151200000, 4870182240, 165589522560, 5970883913280, 228632817853440, 9292843409850000, 400385970127503360, 18252778818295082880, 878619947953407528960, 44562094805330883023040, 2376296054962478899200000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

FORMULA

E.g.f.: 1/(1-LambertW(-x)^6)^(1/6). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-5/12) * 2^(1/4) * sqrt(Pi) / (3^(1/6) * GAMMA(1/12)) * (1 - 85 * sqrt(2/n) * GAMMA(1/12) / (432 * GAMMA(7/12))). - 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+6)*(i-1)!^j*

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

    end:

a:= a->add(b(j, 6)*n^(n-j)*binomial(n-1, j-1), j=0..n):

seq(a(n), n=0..25);

MATHEMATICA

CoefficientList[Series[1/(1-LambertW[-x]^6)^(1/6), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

CROSSREFS

Column k=6 of A246609.

Sequence in context: A140907 A072419 A246193 * A031145 A126245 A221435

Adjacent sequences:  A246610 A246611 A246612 * A246614 A246615 A246616

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2014

STATUS

approved

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Last modified January 19 21:31 EST 2022. Contains 350466 sequences. (Running on oeis4.)