A379382 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^2) ).

1, 2, 8, 48, 336, 2560, 20608, 172416, 1484288, 13062144, 116977664, 1062600704, 9767067648, 90673700864, 848971661312, 8007542571008, 76014137180160, 725681289822208, 6962697126019072, 67105309925048320, 649362348326256640, 6306663216709632000

Offset: 0

Author

Seiichi Manyama, Dec 22 2024

Keywords

• nonn

Crossrefs

Cf. A138020, A379383.

Cf. A151374, A379327, A379330.

Cf. A106228.

Programs

PARI

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

Formula

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

a(n) = 2^n * A106228(n).