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%I #9 Oct 05 2023 08:39:35
%S 1,1,7,42,287,2114,16338,130802,1075355,9025656,77021482,666267502,
%T 5829209046,51492030953,458612500526,4113879873624,37133888342707,
%U 337041718357465,3074153880004188,28162578841220534,259020296989987934,2390818256963083305
%N G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^4*A(x)^3.
%F a(n) = Sum_{k=0..n} binomial(4*k,n-k) * binomial(3*k,k)/(2*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(4*k, n-k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A364475, A366200, A366221.
%Y Cf. A099235, A360082.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 04 2023