cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A340562 a(n) = Product_{1<=j,k<=n-1} (4*sin(j*Pi/n)^2 + 4*sin(k*Pi/n)^2).

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%I A340562 #14 Feb 28 2023 23:48:08
%S A340562 1,8,1296,2654208,62500000000,16314248724480000,
%T A340562 46246966018211028668416,1405124434459231021756179283968,
%U A340562 453518708737693704370173592484540645376,1545285638496177620571506637671497728000000000000
%N A340562 a(n) = Product_{1<=j,k<=n-1} (4*sin(j*Pi/n)^2 + 4*sin(k*Pi/n)^2).
%F A340562 a(n) = A212800(n)/n^2.
%F A340562 a(n) ~ Gamma(1/4)^4 * exp(4*G*n^2/Pi) / (16 * Pi^3 * n^2), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Feb 14 2021
%t A340562 Table[Product[4*Sin[j*Pi/n]^2 + 4*Sin[k*Pi/n]^2, {k, 1, n-1}, {j, 1, n-1}], {n, 1, 12}] // Round (* _Vaclav Kotesovec_, Feb 14 2021 *)
%o A340562 (PARI) default(realprecision, 120);
%o A340562 {a(n) = round(prod(j=1, n-1, prod(k=1, n-1, 4*sin(j*Pi/n)^2+4*sin(k*Pi/n)^2)))}
%Y A340562 Main diagonal of A340560.
%Y A340562 Cf. A212800.
%K A340562 nonn
%O A340562 1,2
%A A340562 _Seiichi Manyama_, Jan 11 2021