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%I #12 Feb 18 2023 19:57:52
%S 1,1,4,27,257,3141,46899,827639,16855357,389100834,10040378183,
%T 286386193685,8947506702834,303875954083536,11146559606379269,
%U 439178938765108083,18497974976610341624,829420114454360154295,39445018962975879216867
%N Expansion of Sum_{k>=0} (k * x * (1 + k*x^3))^k.
%H Winston de Greef, <a href="/A360731/b360731.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = Sum_{k=0..floor(n/4)} (n-3*k)^(n-2*k) * binomial(n-3*k,k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+k*x^3))^k))
%o (PARI) a(n) = sum(k=0, n\4, (n-3*k)^(n-2*k)*binomial(n-3*k, k));
%Y Cf. A360618, A360730.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 18 2023
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