A372090 G.f. A(x) satisfies A(x) = 1/( 1 - 4*x*A(x)*(1 + x*A(x)) )^(1/2).

1, 2, 12, 88, 728, 6464, 60192, 579968, 5733728, 57834496, 592831616, 6157627392, 64667721472, 685526908928, 7325711938560, 78832088481792, 853511147742720, 9290927259254784, 101623578654689280, 1116343335709048832, 12310726500144599040

Offset: 0

Author

Seiichi Manyama, Apr 17 2024

Keywords

• nonn

Crossrefs

Cf. A372091.

Programs

PARI

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

Formula

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

a(n) = 4^n*binomial((3*n-1)/2, n)*hypergeom([(1-n)/2, -n/2], [(1-3*n)/2], -1)/(n+1). - Stefano Spezia, Apr 18 2024