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

%I A358387 #8 Jan 08 2024 05:24:07
%S A358387 1,9,117,2457,60669,1620729,45385461,1311647913,38774378493,
%T A358387 1165936210281,35529105456117,1094291069720121,34000718751227133,
%U A358387 1064200845293945433,33516300131277352821,1061218377653812515657,33757038339556757274621,1078167326486278065165513
%N A358387 a(n) = 3 * h(n - 1) * h(n) for n >= 1, where h(n) = hypergeom([-n, -n], [1], 2), and a(0) = 1.
%F A358387 a(n) ~ 3*sqrt(2) * (1 + sqrt(2))^(4*n) / (8*Pi*n). - _Vaclav Kotesovec_, Jan 08 2024
%p A358387 h := n -> hypergeom([-n, -n], [1], 2):
%p A358387 A358387 := n -> ifelse(n = 0, 1, 3*h(n-1)*h(n)):
%p A358387 seq(simplify(A358387(n)), n = 0..17);
%o A358387 (Python)
%o A358387 def A358387gen() -> Generator:
%o A358387     b, a, n = 1, 3, 1
%o A358387     yield b
%o A358387     while True:
%o A358387         yield  3 * a * b
%o A358387         n += 1
%o A358387         aa = a * (6 * n - 3)
%o A358387         bb = b * (n - 1)
%o A358387         b, a = a, (aa - bb) // n
%o A358387 A358387 = A358387gen()
%o A358387 print([next(A358387) for n in range(18)])
%Y A358387 Cf. A358388.
%K A358387 nonn
%O A358387 0,2
%A A358387 _Peter Luschny_, Nov 15 2022