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A246530 Number of endofunctions on [n] whose cycle lengths are divisors of 10.

%I A246530 #5 Aug 28 2014 20:57:55
%S A246530 1,1,4,25,218,2475,34696,579223,11220540,247395097,6117023600,
%T A246530 167639670441,5044046990776,165322086357715,5863394794421088,
%U A246530 223751099288794375,9141963589243198736,398198217292835137137,18420080017512816009280,901874615547758970425977
%N A246530 Number of endofunctions on [n] whose cycle lengths are divisors of 10.
%H A246530 Alois P. Heinz, <a href="/A246530/b246530.txt">Table of n, a(n) for n = 0..350</a>
%F A246530 E.g.f.: exp(Sum_{d|10} (-LambertW(-x))^d/d).
%p A246530 with(numtheory):
%p A246530 egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
%p A246530 a:= n-> n!*coeff(series(egf(10), x, n+1), x, n):
%p A246530 seq(a(n), n=0..25);
%p A246530 # second Maple program:
%p A246530 with(combinat):
%p A246530 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246530       add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*
%p A246530       (i-1)!^j, j=0..`if`(irem(10, i)=0, n/i, 0))))
%p A246530     end:
%p A246530 a:= n-> add(b(j, min(10, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A246530 seq(a(n), n=0..25);
%Y A246530 Column k=10 of A246522.
%K A246530 nonn
%O A246530 0,3
%A A246530 _Alois P. Heinz_, Aug 28 2014