A358387 a(n) = 3 * h(n - 1) * h(n) for n >= 1, where h(n) = hypergeom([-n, -n], [1], 2), and a(0) = 1.

1, 9, 117, 2457, 60669, 1620729, 45385461, 1311647913, 38774378493, 1165936210281, 35529105456117, 1094291069720121, 34000718751227133, 1064200845293945433, 33516300131277352821, 1061218377653812515657, 33757038339556757274621, 1078167326486278065165513

Offset: 0

Author

Peter Luschny, Nov 15 2022

Keywords

• nonn

Crossrefs

Cf. A358388.

Programs

Maple

h := n -> hypergeom([-n, -n], [1], 2):
A358387 := n -> ifelse(n = 0, 1, 3*h(n-1)*h(n)):
seq(simplify(A358387(n)), n = 0..17);

Python

def A358387gen() -> Generator:
    b, a, n = 1, 3, 1
    yield b
    while True:
        yield  3 * a * b
        n += 1
        aa = a * (6 * n - 3)
        bb = b * (n - 1)
        b, a = a, (aa - bb) // n
A358387 = A358387gen()
print([next(A358387) for n in range(18)])

Formula

a(n) ~ 3*sqrt(2) * (1 + sqrt(2))^(4*n) / (8*Pi*n). - Vaclav Kotesovec, Jan 08 2024