This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371644 #4 Mar 31 2024 07:48:57
%S A371644 1,1,10,57915,8235313944000,1077099640691257742845893750,
%T A371644 4629575796245443900868634734946423885068807034000
%N A371644 a(n) = Product_{k=0..n} binomial(n^2 + k^2, n^2 - k^2).
%F A371644 a(n) = A371642(n) / A371645(n).
%F A371644 a(n) = A371643(n) / (A371624(n) * A371645(n)).
%F A371644 a(n) ~ c * exp(Pi*n^3/3 + Pi*n/4 + n) / (2^(2*n^3/3 + 3*n/2) * Pi^(n/2) * A^(2*n) * n^(7*n/6 - 1/4)), where c = 0.761512... = 2^(1/4) * A255504 * (c from A371603) / (c from A371645) and A is the Glaisher-Kinkelin constant A074962.
%t A371644 Table[Product[Binomial[n^2+k^2, n^2-k^2], {k, 0, n}], {n, 0, 8}]
%Y A371644 Cf. A371603, A371624, A371642, A371643, A371645.
%K A371644 nonn
%O A371644 0,3
%A A371644 _Vaclav Kotesovec_, Mar 31 2024