A371518 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^2.

1, 2, 11, 72, 525, 4104, 33647, 285526, 2486809, 22103726, 199697284, 1828472914, 16929944932, 158246198836, 1491210732346, 14151603542612, 135130396860130, 1297381593071890, 12516650939119421, 121281286192026308, 1179769340479567499

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349331, A371483, A371517.

Cf. A270386, A371523.

Programs

PARI

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

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349331.