%I #5 Aug 28 2014 20:18:25

%S 1,1,3,16,125,1296,16807,262864,4829049,102073600,2441582891,

%T 65201946624,1922453391157,62009850843136,2171369477933775,

%U 82007515430081536,3322113623606686193,143662773881554108416,6604529623711334804179,321608928954695680000000

%N Number of endofunctions on [n] whose cycle lengths are divisors of 7.

%H Alois P. Heinz, <a href="/A246527/b246527.txt">Table of n, a(n) for n = 0..350</a>

%F E.g.f.: exp(Sum_{d|7} (-LambertW(-x))^d/d).

%p with(numtheory):

%p egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):

%p a:= n-> n!*coeff(series(egf(7), x, n+1), x, n):

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

%p # second Maple program:

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*

%p (i-1)!^j, j=0..`if`(irem(7, i)=0, n/i, 0))))

%p end:

%p a:= n-> add(b(j, min(7, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):

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

%Y Column k=7 of A246522.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 28 2014