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%I #13 Oct 03 2023 09:00:04
%S 1,4,18,112,847,7086,62974,583002,5560323,54249583,538873135,
%T 5431177821,55402340842,570899082760,5933922697380,62138800690564,
%U 654949976467593,6942859160218698,73972792893687427,791722414873487767,8508265804914763731
%N G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^3.
%H Seiichi Manyama, <a href="/A364623/b364623.txt">Table of n, a(n) for n = 0..944</a>
%F a(n) = Sum_{k=0..n} binomial(n+5*k+2,6*k+2) * binomial(3*k,k) / (2*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+5*k+2, 6*k+2)*binomial(3*k, k)/(2*k+1));
%Y Partial sums of A364629.
%Y Cf. A162481, A364624.
%Y Cf. A001764, A199475, A364620.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 30 2023
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