A377239 Expansion of sqrt(1 + 4*x/sqrt(1 - 4*x)).

1, 2, 2, 8, 22, 80, 268, 976, 3494, 12896, 47556, 177744, 666236, 2515104, 9525976, 36240032, 138269958, 529193152, 2030242708, 7807266512, 30082317460, 116126074400, 449014896040, 1738805527520, 6742758295900, 26180338089280, 101769629532968, 396031222808096, 1542673037902904

Offset: 0

Author

Seiichi Manyama, Oct 21 2024

Keywords

• nonn

Crossrefs

Cf. A377240.

Programs

PARI

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

Formula

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

a(n) ~ 2^(2*n) / (Gamma(1/4) * n^(3/4)) * (1 - Gamma(1/4)^2 / (Pi*2^(7/2)*sqrt(n))). - Vaclav Kotesovec, May 03 2025