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A246241 Sum of sixth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.

%I A246241 #4 Aug 19 2014 20:14:18
%S A246241 1,1,66,51033,227263876,3942914312505,207874071367118436,
%T A246241 28034487027123336138967,8522964991458712709499563784,
%U A246241 5302659152501095787067079018931409,6255441983177258421672575234559926069140,13154762734940720943667470423246456789300752691
%N A246241 Sum of sixth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.
%H A246241 Alois P. Heinz, <a href="/A246241/b246241.txt">Table of n, a(n) for n = 0..100</a>
%F A246241 a(n) = [x^n] (n!)^6 * (Sum_{j=0..n} x^j/(j!)^6)^n.
%p A246241 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246241       add(b(n-j, i-1)*binomial(n, j)^5/j!, j=0..n)))
%p A246241     end:
%p A246241 a:= n-> n!*b(n$2):
%p A246241 seq(a(n), n=0..15);
%Y A246241 Column k=6 of A245397.
%K A246241 nonn
%O A246241 0,3
%A A246241 _Alois P. Heinz_, Aug 19 2014