A364593 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^3.

1, 1, 2, 3, 7, 14, 36, 85, 228, 587, 1612, 4354, 12166, 33832, 95876, 271803, 779287, 2239584, 6483386, 18823945, 54932299, 160771540, 472322632, 1391323310, 4110685812, 12173949214, 36141795088, 107521223008, 320531857144, 957289637952, 2864055208772

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

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

Prog

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

Crossrefs

Cf. A110199, A364594.

Sequence in context: A006660 A306844 A213906 * A123777 A245899 A246747

Adjacent sequences: A364590 A364591 A364592 * A364594 A364595 A364596

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved