A358387 - OEIS

%I #8 Jan 08 2024 05:24:07

%S 1,9,117,2457,60669,1620729,45385461,1311647913,38774378493,

%T 1165936210281,35529105456117,1094291069720121,34000718751227133,

%U 1064200845293945433,33516300131277352821,1061218377653812515657,33757038339556757274621,1078167326486278065165513

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

%F a(n) ~ 3*sqrt(2) * (1 + sqrt(2))^(4*n) / (8*Pi*n). - _Vaclav Kotesovec_, Jan 08 2024

%p h := n -> hypergeom([-n, -n], [1], 2):

%p A358387 := n -> ifelse(n = 0, 1, 3*h(n-1)*h(n)):

%p seq(simplify(A358387(n)), n = 0..17);

%o (Python)

%o def A358387gen() -> Generator:

%o     b, a, n = 1, 3, 1

%o     yield b

%o     while True:

%o         yield  3 * a * b

%o         n += 1

%o         aa = a * (6 * n - 3)

%o         bb = b * (n - 1)

%o         b, a = a, (aa - bb) // n

%o A358387 = A358387gen()

%o print([next(A358387) for n in range(18)])

%Y Cf. A358388.

%K nonn

%O 0,2

%A _Peter Luschny_, Nov 15 2022