A379191 G.f. A(x) satisfies A(x) = (1 + x*A(x))^3/(1 - x*A(x)^3).

1, 4, 31, 338, 4356, 61603, 923958, 14433315, 232298914, 3825260332, 64140203645, 1091364139213, 18796605318655, 327056343952311, 5740466392321499, 101516213938082457, 1807045676161156515, 32352346658163940698, 582185299986049977601, 10524395285312191583304, 191034444423571726099486

Offset: 0

Author

Seiichi Manyama, Dec 17 2024

Keywords

• nonn

Crossrefs

Cf. A379172, A379188, A379190.

Cf. A307678, A379192.

Programs

PARI

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

Formula

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