A341478 - OEIS

%I #17 Feb 28 2023 23:48:11

%S 1,1,6,112,6664,1270016,776239200,1522266730496,9580300901941376,

%T 193509323594243571712,12545297912843041612924416,

%U 2610531939025273190037188509696,1743627211475190637398673259679582208

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

%F a(n) ~ exp(2*G*n^2/Pi) / 2^(3/4), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Feb 14 2021

%t Table[Sqrt[Product[4*Sin[j*Pi/n]^2 + 4*Sin[(2*k - 1)*Pi/(2*n)]^2, {k, 1, n}, {j, 1, n-1}]], {n, 0, 15}] // Round (* _Vaclav Kotesovec_, Feb 14 2021 *)

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

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

%Y Cf. A335586, A340562, A341479, A341493.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 13 2021