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%I #27 Feb 28 2023 23:46:52
%S 1,6,500,463736,4614756624,485005220494432,533978739649683515200,
%T 6129678550595328659594928000,731483813983605533022316212534132992,
%U 905665520470954445892575061753881157482726912
%N a(n) = 2^(2*n*n) * Product_{i=1..n} Product_{j=1..n} (sin(i*Pi/(2*n+1))^2 + sin(j*Pi/(2*n+1))^2).
%F a(n) ~ Gamma(1/4) * exp(G*(2*n+1)^2/Pi) / (2^(3/2) * Pi^(3/4) * sqrt(n)), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Dec 30 2020
%p for n from 0 to 12 do a[n]:=2^(2*n*n)*product(product(sin(i*Pi/(2*n+1))^2+ sin(j*Pi/(2*n+1))^2,j=1..n),i=1..n) od: seq(round(evalf(a[n],300)),n=0..12);
%t Table[(2*n+1) * 2^(n*(2*n-1)) * Product[Product[Sin[i*Pi/(2*n + 1)]^2 + Sin[j*Pi/(2*n + 1)]^2, {i, 1, j-1}], {j, 2, n}]^2, {n, 0, 15}] // Round (* _Vaclav Kotesovec_, Dec 30 2020 *)
%Y Cf. A004003, A007341, A340052.
%K nonn
%O 0,2
%A _Miklos Kristof_, Apr 03 2007