A366180 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x)^3.

1, 3, 15, 109, 909, 8184, 77626, 764226, 7735878, 80011063, 841875232, 8983175079, 96977392945, 1057262750608, 11623867926024, 128730566729686, 1434752590885174, 16080839356274157, 181135636330594960, 2049430159361529977, 23280997677471432102

Offset: 0

Author

Seiichi Manyama, Oct 03 2023

Keywords

• nonn

Crossrefs

Partial sums give A366182.

Cf. A364620, A364629, A366179.

Programs

PARI

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

Formula

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