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%I #19 Feb 28 2023 23:47:37
%S 1,7,4961,371647151,2952717950351617,2489597262406609716450871,
%T 222812636926792555435326125877303201,
%U 2116840405025957772469476908228785308996001314527,2134958300495920487325052422663717579194357002081033470045923329
%N a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * sin(k*Pi/(2*n+1))^2).
%F a(n) = A002315(n) * A340293(n)^2.
%F a(n) ~ exp(2*G*(2*n+1)^2/Pi) / 2^(4*n + 3/4), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Jan 04 2021
%t Table[2^(4*n^2) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2 * Sin[k*Pi/(2*n + 1)]^2, {k, 1, n}], {j, 1, n}], {n, 0, 10}] // Round (* _Vaclav Kotesovec_, Jan 04 2021 *)
%o (PARI) default(realprecision, 120);
%o {a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(sin(j*Pi/(2*n+1))*sin(k*Pi/(2*n+1)))^2)))}
%Y Cf. A002315, A340166, A340291, A340293, A340295.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 03 2021
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