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%I #9 Apr 01 2024 09:39:22
%S 1,2,806400,29900785676206001356800000,
%T 1118776785681133797769642926006209350326602179759885516800000000000000
%N a(n) = Product_{k=0..n} (n^2 + k^2)! / (n^2 - k^2)!.
%F a(n) = A371643(n) / A371624(n).
%F a(n) ~ c * 2^(n^2 - n/6 + 1/4) * exp((3*Pi-10)*n^3/9 - n^2 + Pi*n/4) * n^(4*n^3/3 + 2*n^2 + n/2 + 3/4) / A^(2*n), where c = 1.941002... = A255504 * (c from A371603) and A is the Glaisher-Kinkelin constant A074962.
%t Table[Product[(n^2+k^2)!/(n^2-k^2)!, {k, 0, n}], {n, 0, 6}]
%Y Cf. A272241, A371624, A371643.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 31 2024
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