login
G.f. A(x) satisfies A(x) = 1/(1 - x) + x*A(x)^3/(1 - x)^3.
2

%I #9 Oct 03 2023 09:00:00

%S 1,2,10,67,502,4045,34279,301232,2720266,25091431,235394601,

%T 2239139980,21546299491,209361514219,2051379996574,20245794958408,

%U 201079938971546,2008276118393320,20157131084034349,203215717750220949,2056913539436637829

%N G.f. A(x) satisfies A(x) = 1/(1 - x) + x*A(x)^3/(1 - x)^3.

%F a(n) = Sum_{k=0..n} binomial(n+4*k,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+4*k, n-k)*binomial(3*k, k)/(2*k+1));

%Y Partial sums give A366179.

%Y Cf. A199475, A346626, A366177.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 03 2023