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Expansion of Sum_{k>=0} x^k / (1 - (k*x)^3)^(k+1).
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%I #9 Feb 20 2023 12:27:33

%S 1,1,1,1,3,25,109,324,1135,8803,64189,337854,1707319,13421410,

%T 121248893,894378619,6082868725,53046554917,543432115477,

%U 4989423130739,42565774604131,421544374075072,4781440892689533,51342685464272591,522295380717090265

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

%F a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(3*k) * binomial(n-2*k,k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^3)^(k+1)))

%o (PARI) a(n) = sum(k=0, n\3, (n-3*k)^(3*k)*binomial(n-2*k, k));

%Y Cf. A000248, A360787.

%Y Cf. A360783.

%K nonn,easy

%O 0,5

%A _Seiichi Manyama_, Feb 20 2023