A364645 G.f. satisfies A(x) = 1/(1 - 3*x) - x*A(x)^3.

1, 2, 3, 6, 19, 51, 114, 312, 981, 2616, 6564, 19647, 59922, 159056, 430302, 1329996, 3926217, 10498968, 30052851, 93244764, 267690168, 729649143, 2173840338, 6663260223, 18768583674, 52570016676, 160362713250, 481809941520, 1346473504182, 3886164785178

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Prog

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

Crossrefs

Cf. A364641, A364646, A364647.

Cf. A005773, A349254, A349256, A349534.

Sequence in context: A000614 A233239 A018290 * A182250 A121959 A075633

Adjacent sequences: A364642 A364643 A364644 * A364646 A364647 A364648

Keyword

nonn

Author

Seiichi Manyama, Jul 31 2023

Status

approved