%I #10 Oct 17 2023 08:34:23
%S 1,4,19,173,1860,21814,271388,3515330,46906860,640321565,8899950644,
%T 125524292790,1791943900656,25843064347685,375956017001280,
%U 5510454405453368,81297696816798684,1206334991431968912,17991734573723974384,269560224872407933010
%N G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^4.
%F a(n) = Sum_{k=0..n} binomial(3*(3*k+1),n-k) * binomial(4*k,k)/(3*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(3*(3*k+1), n-k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A366267, A366698, A366700.
%Y Cf. A364624.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 16 2023