A379244 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3)/(1 - x*A(x)) )^2.

1, 4, 40, 540, 8400, 141876, 2528760, 46815116, 891483808, 17350187364, 343578992328, 6900588813564, 140230648164720, 2878066866407316, 59571280942854808, 1242093725341221996, 26064579113472078144, 550041399791036747460, 11665771061882347813224, 248527169321049466503132

Offset: 0

Author

Seiichi Manyama, Dec 18 2024

Keywords

• nonn

Crossrefs

Cf. A032349, A371675.

Cf. A364167, A379174.

Programs

PARI

a(n) = sum(k=0, n, binomial(2*n+4*k+2, k)*binomial(3*n+3*k+1, n-k)/(n+2*k+1));

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A364167.

a(n) = Sum_{k=0..n} binomial(2*n+4*k+2,k) * binomial(3*n+3*k+1,n-k)/(n+2*k+1).