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%I #7 Jul 17 2020 22:24:16
%S 1,1,33,8263,8718945,28076306251,224968772934303,3896175006605313013,
%T 131557135159637950535265,8004845815916146011992853811,
%U 824857614282973828473497207276283,136888961901974254918775560412316183913,35099479542762449254288789631427310686677535
%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^5 * a(k).
%H Seiichi Manyama, <a href="/A336197/b336197.txt">Table of n, a(n) for n = 0..120</a>
%F a(n) = (n!)^5 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^5).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^5 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]
%t nmax = 12; CoefficientList[Series[1/(1 - Sum[x^k/(k!)^5, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^5
%Y Column k=5 of A326322.
%Y Cf. A000670, A102221, A336195, A336196.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 11 2020
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