A379256 - OEIS

%I #6 Dec 19 2024 10:10:12

%S 1,2,20,296,5168,98896,2006592,42403584,923292672,20570204672,

%T 466681402112,10744734700032,250415336695808,5896251565619200,

%U 140051037257007104,3351752341884928000,80744484314316193792,1956433860220223062016,47647871136991576260608

%N G.f. A(x) satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x)^4).

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

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

%Y Cf. A379257.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 19 2024