A379190 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x*A(x))^3.

1, 4, 30, 304, 3557, 45150, 604222, 8393282, 119872890, 1749183075, 25964512607, 390828464403, 5951561595889, 91523131078999, 1419293428538496, 22169968253466467, 348507676062911520, 5509187208564734328, 87522347516801353980, 1396619714730284551913, 22375420057050167868366

Offset: 0

Author

Seiichi Manyama, Dec 17 2024

Keywords

• nonn

Crossrefs

Cf. A379172, A379188, A379191.

Cf. A002293, A274735, A364475.

Cf. A198953.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(3*n+6*k+3, n-k)/(n+2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(3*n+6*k+3,n-k)/(n+2*k+1).