A246611 Number of endofunctions on [n] whose cycle lengths are multiples of 4.

1, 0, 0, 0, 6, 120, 2160, 41160, 866460, 20294064, 526680000, 15036999120, 468848156040, 15859299473160, 578619457031616, 22654279249875000, 947570269816868880, 42174922731482980320, 1990416896317283627520, 99290011292792071612704, 5220362654145754082460000

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 A356506

Adjacent sequences: A246608 A246609 A246610 * A246612 A246613 A246614

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved