A379209 G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))).

1, 2, 9, 53, 357, 2605, 20041, 160074, 1314821, 11036015, 94242752, 816190963, 7151741597, 63287390223, 564791911903, 5077284164245, 45935201005749, 417928249605123, 3821430547469626, 35098466575407095, 323662850948066340, 2995524340795970120

Offset: 0

Author

Seiichi Manyama, Dec 18 2024

Keywords

• nonn

Crossrefs

Cf. A006013, A379189.

Cf. A190738.

Programs

PARI

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

Formula

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

a(n) = A190738(n)/(n+1).