|
%I #18 Feb 28 2023 23:47:33
%S 1,15,32625,8238791743,230629380093001665,703130165949449759361247759,
%T 231459008314298532714943209968328640625,
%U 8186710889725936196671113787217620194601044287109375
%N a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - cos(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).
%F a(n) = A093967(2*n+1) * A340185(n)^2.
%F a(n) ~ Gamma(1/4) * exp(2*G*(2*n+1)^2/Pi) / (Pi^(3/4) * sqrt(n) * 2^(2*n + 2)), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Jan 03 2021
%t Table[2^(4*n^2) * Product[Product[1 - Cos[j*Pi/(2*n+1)]^2 * Cos[k*Pi/(2*n+1)]^2, {j, 1, n}], {k, 1, n}], {n, 0, 10}] // Round (* _Vaclav Kotesovec_, Jan 03 2021 *)
%o (PARI) default(realprecision, 120);
%o {a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(cos(j*Pi/(2*n+1))*cos(k*Pi/(2*n+1)))^2)))}
%Y Cf. A093967, A340166, A340185, A340292, A340295.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 03 2021
|
