A340293 - OEIS

%I #16 Feb 28 2023 23:48:45

%S 1,1,11,1247,1455913,17511093953,2169916151129091,

%T 2770393222231417622719,36443188794328204864735075793,

%U 4939371777650229260975457785579794433,6897784079863728378183626237683602071537213179

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

%F a(n) ~ exp(G*(2*n+1)^2/Pi) / (2^(2*n - 1/8) * (1 + sqrt(2))^(n + 1/2)), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Jan 04 2021

%t Table[2^(2*n*(n-1)) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2*Sin[k*Pi/(2*n + 1)]^2, {k, j+1, n}], {j, 1, n}], {n, 0, 12}] // Round (* _Vaclav Kotesovec_, Jan 04 2021 *)

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

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

%Y Cf. A340185, A340292.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 03 2021