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%I #8 Jul 17 2020 22:34:12
%S 1,1,9,271,19353,2699251,650553183,248978967973,142238892608025,
%T 115699539306013867,129097362200437841259,191726066802105786953113,
%U 369666963359241578736653775,906204961889202975320635813201,2774573804997927027583123365125685
%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^3 * a(k).
%H Seiichi Manyama, <a href="/A336195/b336195.txt">Table of n, a(n) for n = 0..180</a>
%F a(n) = (n!)^3 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^3).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^3 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
%t nmax = 14; CoefficientList[Series[1/(1 - Sum[x^k/(k!)^3, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3
%Y Column k=3 of A326322.
%Y Cf. A000670, A102221, A336196, A336197.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 11 2020
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