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A355469 Expansion of Sum_{k>=0} (k^3 * x/(1 - k^3 * x))^k.

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%I A355469 #13 Feb 21 2023 23:24:56
%S A355469 1,1,65,20708,18383828,34898769936,121324513279512,697408243146701056,
%T A355469 6165037130760825320768,79390334273383043609851520,
%U A355469 1428007543233019703635181454080,34693490969752778534655707874499584,1107666867764009444258160579726602423808
%N A355469 Expansion of Sum_{k>=0} (k^3 * x/(1 - k^3 * x))^k.
%H A355469 Winston de Greef, <a href="/A355469/b355469.txt">Table of n, a(n) for n = 0..151</a>
%F A355469 a(n) = Sum_{k=1..n} k^(3*n) * binomial(n-1,k-1) for n > 0.
%o A355469 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x/(1-k^3*x))^k))
%o A355469 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(3*n)*binomial(n-1, k-1)));
%Y A355469 Cf. A355468, A355470.
%K A355469 nonn
%O A355469 0,3
%A A355469 _Seiichi Manyama_, Jul 03 2022