A379037 G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(3/2)) )^2.

1, 4, 18, 106, 689, 4782, 34707, 260190, 1999168, 15660176, 124596498, 1004110948, 8179379807, 67239070868, 557098881919, 4647368670950, 39001655222787, 329048378867468, 2789241880512898, 23743798316713368, 202894843070927859, 1739775692700850554

Offset: 0

Author

Seiichi Manyama, Dec 14 2024

Keywords

• nonn

Crossrefs

Cf. A004798, A073155, A379039.

Cf. A364336, A366200.

Programs

PARI

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

Formula

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A364336.

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