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%I #9 Jul 29 2023 10:49:47
%S 1,1,2,3,7,14,36,85,228,587,1612,4354,12166,33832,95876,271803,779287,
%T 2239584,6483386,18823945,54932299,160771540,472322632,1391323310,
%U 4110685812,12173949214,36141795088,107521223008,320531857144,957289637952,2864055208772
%N G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^3.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(3*k,k) / (2*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A110199, A364594.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jul 29 2023
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