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%I #4 Aug 19 2014 20:25:16
%S 1,1,258,1718985,115245958660,46377854607812505,
%T 80785609177262537107236,486005483266096999009285275991,
%U 8558639841332633529404511878004186120,388791577542234912413815089860741309780872785,41231194444310047390596429351583294775856761836687780
%N Sum of eighth powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.
%H Alois P. Heinz, <a href="/A246243/b246243.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = [x^n] (n!)^8 * (Sum_{j=0..n} x^j/(j!)^8)^n.
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(b(n-j, i-1)*binomial(n, j)^7/j!, j=0..n)))
%p end:
%p a:= n-> n!*b(n$2):
%p seq(a(n), n=0..15);
%Y Column k=8 of A245397.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 19 2014