A381875 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108.

1, 3, 13, 66, 368, 2185, 13570, 87147, 574241, 3861286, 26390591, 182798850, 1280387583, 9053335674, 64534088960, 463249047099, 3345832486407, 24296575830677, 177286818019264, 1299208549351640, 9557974679439901, 70563100013789595, 522608148884843970

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = binomial(1 + 3*n, n)*hypergeom([-1/2-n, -n, 1+n], [-1/3-n, 1/3-n], 2^2/3^3)/(1 + n). - Stefano Spezia, Mar 09 2025

Prog

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

Crossrefs

Cf. A129442, A381876, A381877.

Cf. A000108.

Sequence in context: A219537 A394119 A045743 * A110530 A142979 A302303

Adjacent sequences: A381872 A381873 A381874 * A381876 A381877 A381878

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2025

Status

approved