A367040 G.f. satisfies A(x) = 1 + x^2 + x*A(x)^3.

1, 1, 4, 15, 70, 360, 1953, 11008, 63837, 378390, 2282205, 13960890, 86411232, 540166219, 3405341160, 21625820793, 138216775785, 888371346825, 5738510504979, 37234351046835, 242567430368298, 1585979835198675, 10403866383915844, 68453912880893025

Offset: 0

Author

Seiichi Manyama, Nov 03 2023

Keywords

• nonn

Crossrefs

Cf. A176697, A367041.

Cf. A366266, A366676.

Cf. A002293, A104979, A186997, A255673, A361245, A364474, A364475, A364478.

Programs

PARI

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

Formula

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