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Sum of seventh powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.
2

%I #4 Aug 19 2014 20:21:16

%S 1,1,130,293061,5018329348,414999981562505,124389170238814179336,

%T 110807909819808911886548575,253626563859350391170222920686088,

%U 1334380576777390115212093953972864348177,14777734823564325121187478504310896072495827020

%N Sum of seventh powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n.

%H Alois P. Heinz, <a href="/A246242/b246242.txt">Table of n, a(n) for n = 0..90</a>

%F a(n) = [x^n] (n!)^7 * (Sum_{j=0..n} x^j/(j!)^7)^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)^6/j!, j=0..n)))

%p end:

%p a:= n-> n!*b(n$2):

%p seq(a(n), n=0..15);

%Y Column k=7 of A245397.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 19 2014