%I #16 Oct 11 2023 08:40:08
%S 1,1,7,49,399,3521,32767,316673,3147775,31977985,330544639,3465369601,
%T 36759599103,393820102657,4255079743487,46313023946753,
%U 507319247208447,5588706552643585,61875364144283647,688128167799619585,7683686768042639359
%N G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^3*A(x)^4.
%F a(n) = Sum_{k=0..n} binomial(3*k,n-k) * binomial(4*k,k)/(3*k+1).
%F G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366436.
%o (PARI) a(n) = sum(k=0, n, binomial(3*k, n-k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A052709, A366221, A366273.
%Y Cf. A366267, A366436.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 06 2023