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A246240 Sum of fifth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.

%I A246240 #7 Aug 19 2014 20:08:24
%S A246240 1,1,34,9237,11007556,41262262505,393602334214536,8250608306349317503,
%T A246240 341379009411431516029576,25693424488177173143564108049,
%U A246240 3298778490446719483156753593432700,686045693667123232536420797701863401231,221475400673152122602874526565943771742514376
%N A246240 Sum of fifth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.
%H A246240 Alois P. Heinz, <a href="/A246240/b246240.txt">Table of n, a(n) for n = 0..100</a>
%F A246240 a(n) = [x^n] (n!)^5 * (Sum_{j=0..n} x^j/(j!)^5)^n.
%p A246240 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246240       add(b(n-j, i-1)*binomial(n, j)^4/j!, j=0..n)))
%p A246240     end:
%p A246240 a:= n-> n!*b(n$2):
%p A246240 seq(a(n), n=0..15);
%Y A246240 Column k=5 of A245397.
%K A246240 nonn
%O A246240 0,3
%A A246240 _Alois P. Heinz_, Aug 19 2014