A340165 - OEIS

%I #19 Jan 05 2021 08:52:37

%S 1,1,19,7056,51251277,7280323311888,20225477546584790663,

%T 1098876823994281426921193472,1167619533875635661974056722756222809,

%U 24263631353490502503207804571072304043237024000

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

%F a(n) = 4^((n-2)*(n-1)) * Product_{1<=i<j<=n-1} (1 + cos(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2).

%F a(n) ~ 2^(2*n^2 - 3*n + 35/8) * (1 - sqrt(2*sqrt(2)-2))^n * exp(2*A340350*n^2/Pi^2). - _Vaclav Kotesovec_, Jan 05 2021

%t Table[4^((n-2)*(n-1)) * Product[Product[1 + Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, j-1}], {j, 2, n-1}], {n, 1, 12}] // Round (* _Vaclav Kotesovec_, Dec 31 2020 *)

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

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

%Y Cf. A340139, A340167.

%K nonn

%O 1,3

%A _Seiichi Manyama_, Dec 30 2020