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A355472 Expansion of Sum_{k>=0} (x/(1 - k^3 * x))^k.

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%I A355472 #10 Feb 21 2023 20:58:25
%S A355472 1,1,2,18,275,6680,258897,13646776,959706169,88651586048,
%T A355472 10272048320897,1462972094910224,253355867842243905,
%U A355472 52387780870782231424,12745274175326359046785,3615579524073585972982544,1184928928181459098548941633,444427677344332049739011858432
%N A355472 Expansion of Sum_{k>=0} (x/(1 - k^3 * x))^k.
%H A355472 Winston de Greef, <a href="/A355472/b355472.txt">Table of n, a(n) for n = 0..235</a>
%F A355472 a(n) = Sum_{k=1..n} k^(3*(n-k)) * binomial(n-1,k-1) for n > 0.
%o A355472 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^3*x))^k))
%o A355472 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(3*(n-k))*binomial(n-1, k-1)));
%Y A355472 Cf. A080108, A355463, A355471.
%K A355472 nonn
%O A355472 0,3
%A A355472 _Seiichi Manyama_, Jul 03 2022