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%I #7 Sep 01 2014 16:54:10
%S 1,0,0,0,6,120,2160,41160,866460,20294064,526680000,15036999120,
%T 468848156040,15859299473160,578619457031616,22654279249875000,
%U 947570269816868880,42174922731482980320,1990416896317283627520,99290011292792071612704,5220362654145754082460000
%N Number of endofunctions on [n] whose cycle lengths are multiples of 4.
%H Alois P. Heinz, <a href="/A246611/b246611.txt">Table of n, a(n) for n = 0..300</a>
%F E.g.f.: 1/(1-LambertW(-x)^4)^(1/4). - _Vaclav Kotesovec_, Sep 01 2014
%F 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
%p with(combinat):
%p b:= proc(n, i) option remember; `if`(n=0, 1,
%p `if`(i>n, 0, add(b(n-i*j, i+4)*(i-1)!^j*
%p multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
%p end:
%p a:= a->add(b(j, 4)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p seq(a(n), n=0..20);
%t CoefficientList[Series[1/(1-LambertW[-x]^4)^(1/4),{x,0,20}],x] * Range[0,20]! (* _Vaclav Kotesovec_, Sep 01 2014 *)
%Y Column k=4 of A246609.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Aug 31 2014
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