cp's OEIS Frontend

A245398 Sum of n-th powers of coefficients in full expansion of (z_1 + z_2 + ... + z_n)^n.

%I A245398 #13 Jan 27 2023 20:53:05
%S A245398 1,1,6,381,591460,41262262505,207874071367118436,
%T A245398 110807909819808911886548575,8558639841332633529404511878004186120,
%U A245398 124773193097402414339622625011223384066643153613969,431220070110830123225191271755402469908417673177630594034899052340
%N A245398 Sum of n-th powers of coefficients in full expansion of (z_1 + z_2 + ... + z_n)^n.
%H A245398 Alois P. Heinz, <a href="/A245398/b245398.txt">Table of n, a(n) for n = 0..30</a>
%F A245398 a(n) = [x^n] (n!)^n * (Sum_{j=0..n} x^j/(j!)^n)^n.
%F A245398 a(n) = A245397(n,n).
%p A245398 b:= proc(n, i, k) option remember; `if`(n=0 or i=1, 1,
%p A245398       add(b(n-j, i-1, k)*binomial(n, j)^k, j=0..n))
%p A245398     end:
%p A245398 a:= n-> b(n$3):
%p A245398 seq(a(n), n=0..12);
%t A245398 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
%t A245398    Sum[b[n-j, i-1, k]*Binomial[n, j]^(k-1)/j!, {j, 0, n}]]];
%t A245398 a[n_] := n!*b[n, n, n];
%t A245398 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Jun 27 2022, after _Alois P. Heinz_ *)
%Y A245398 Main diagonal of A245397.
%K A245398 nonn
%O A245398 0,3
%A A245398 _Alois P. Heinz_, Jul 21 2014