A372088 G.f. A(x) satisfies A(x) = 1/( 1 - 4*x*(1 + x*A(x)) )^(1/2).

1, 2, 8, 36, 176, 904, 4808, 26240, 146096, 826496, 4737088, 27447936, 160514144, 946139584, 5615411904, 33529225856, 201268922112, 1213912449280, 7352607996160, 44705058498560, 272757529797120, 1669423083509760, 10247263603251200, 63066403179974656

Offset: 0

Author

Seiichi Manyama, Apr 17 2024

Keywords

• nonn

Crossrefs

Cf. A372002.

Programs

PARI

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

Formula

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