A379280 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3) * (1 + x*A(x)) )^2.

1, 4, 38, 500, 7601, 125520, 2187736, 39608616, 737651032, 14040612502, 271931510448, 5341639974490, 106167131932708, 2131125360950758, 43142742495766252, 879810600033569754, 18057207334571432048, 372701480245014988624, 7731178967720860156743

Offset: 0

Author

Seiichi Manyama, Dec 19 2024

Keywords

• nonn

Crossrefs

Cf. A379244, A379252, A379283.

Cf. A364333, A379249.

Programs

PARI

a(n) = sum(k=0, n, binomial(2*n+4*k+2, k)*binomial(2*n+4*k+2, n-k)/(n+2*k+1));

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A364333.

a(n) = Sum_{k=0..n} binomial(2*n+4*k+2,k) * binomial(2*n+4*k+2,n-k)/(n+2*k+1).