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A246611 Number of endofunctions on [n] whose cycle lengths are multiples of 4. 2
1, 0, 0, 0, 6, 120, 2160, 41160, 866460, 20294064, 526680000, 15036999120, 468848156040, 15859299473160, 578619457031616, 22654279249875000, 947570269816868880, 42174922731482980320, 1990416896317283627520, 99290011292792071612704, 5220362654145754082460000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

E.g.f.: 1/(1-LambertW(-x)^4)^(1/4). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-3/8) * sqrt(Pi) / (2^(1/8) * GAMMA(1/8)) * (1 - 11 * sqrt(2/n) * GAMMA(1/8) / (64 * GAMMA(5/8))). - 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+4)*(i-1)!^j*

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

    end:

a:= a->add(b(j, 4)*n^(n-j)*binomial(n-1, j-1), j=0..n):

seq(a(n), n=0..20);

MATHEMATICA

CoefficientList[Series[1/(1-LambertW[-x]^4)^(1/4), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

CROSSREFS

Column k=4 of A246609.

Sequence in context: A223629 A065888 A246191 * A185757 A075844 A029697

Adjacent sequences:  A246608 A246609 A246610 * A246612 A246613 A246614

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2014

STATUS

approved

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Last modified January 20 00:34 EST 2022. Contains 350467 sequences. (Running on oeis4.)