A341782 - OEIS

%I #19 Mar 18 2023 05:38:39

%S 1,1,2,112,2312,1270016,292820000,1522266730496,3772667519238272,

%T 193509323594243571712,5041011532336819845120512,

%U 2610531939025273190037188509696

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

%H Seiichi Manyama, <a href="/A341782/b341782.txt">Table of n, a(n) for n = 0..62</a>

%F If n is odd, a(n) = A341535(n)/2.

%F If n is odd, a(n) = A341478(n).

%F a(n) ~ exp(2*G*n^2/Pi) / (2^(3/4) * (1 + (1 + (-1)^n)/sqrt(2))), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Mar 18 2023

%t Table[Sqrt[Product[Product[(4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[2*k*Pi/n]^2), {j, 1, n}], {k, 1, n - 1}]], {n, 0, 15}] // Round (* _Vaclav Kotesovec_, Mar 18 2023 *)

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

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

%Y Main diagonal of A341738.

%Y Cf. A341478, A341535.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 19 2021