A381867 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108.

1, 3, 10, 44, 239, 1464, 9610, 65946, 466951, 3385259, 24999475, 187385168, 1421901090, 10901237530, 84312106160, 657031204068, 5153954345309, 40663760712441, 322478148002872, 2569086552458460, 20551321340065924, 165009872444132477, 1329352163579556971, 10742386009423170696

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

a(n) = (1 + n)*hypergeom([1/3, 2/3, -n, 2+n], [1, 3/2, 3/2], -3^3/2^4). - Stefano Spezia, Mar 09 2025

Prog

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

Crossrefs

Cf. A188687, A366034.

Cf. A000108.

Sequence in context: A240172 A167995 A000608 * A333018 A259352 A205803

Adjacent sequences: A381864 A381865 A381866 * A381868 A381869 A381870

Keyword

nonn

Author

Seiichi Manyama, Mar 08 2025

Status

approved