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a(n) = Product_{1<=j,k<=n} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/(2*n))^2).
4

%I #18 Feb 28 2023 23:48:15

%S 1,8,256,80000,268435456,9503683872768,3503536769037500416,

%T 13371518717864846127300608,527073330112110826119518513790976,

%U 214344906329057967318939007805581230080000

%N a(n) = Product_{1<=j,k<=n} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/(2*n))^2).

%F a(n) ~ 2 * exp(4*G*n^2/Pi), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Feb 14 2021

%t Table[Product[4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[(2*k - 1)*Pi/(2*n)]^2, {k, 1, n}, {j, 1, n}], {n, 0, 12}] // Round (* _Vaclav Kotesovec_, Feb 14 2021 *)

%o (PARI) default(realprecision, 120);

%o a(n) = round(prod(j=1, n, prod(k=1, n, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/(2*n))^2)));

%Y Cf. A335586, A340562, A341478, A341493.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2021