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A246526 Number of endofunctions on [n] whose cycle lengths are divisors of 6.

%I A246526 #5 Aug 28 2014 17:26:34
%S A246526 1,1,4,27,250,2951,42552,726097,14318908,320511105,8029282096,
%T A246526 222590246099,6765751467576,223748991426247,7998566722112800,
%U A246526 307359039816710361,12634664945078752528,553260940314226017473,25711427896197877574208,1263904006537455579001675
%N A246526 Number of endofunctions on [n] whose cycle lengths are divisors of 6.
%H A246526 Alois P. Heinz, <a href="/A246526/b246526.txt">Table of n, a(n) for n = 0..350</a>
%F A246526 E.g.f.: exp(Sum_{d|6} (-LambertW(-x))^d/d).
%p A246526 with(numtheory):
%p A246526 egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
%p A246526 a:= n-> n!*coeff(series(egf(6), x, n+1), x, n):
%p A246526 seq(a(n), n=0..25);
%p A246526 # second Maple program:
%p A246526 with(combinat):
%p A246526 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246526       add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*
%p A246526       (i-1)!^j, j=0..`if`(irem(6, i)=0, n/i, 0))))
%p A246526     end:
%p A246526 a:= n-> add(b(j, min(6, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A246526 seq(a(n), n=0..25);
%Y A246526 Column k=6 of A246522.
%K A246526 nonn
%O A246526 0,3
%A A246526 _Alois P. Heinz_, Aug 28 2014