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

1, 8, 1296, 2654208, 62500000000, 16314248724480000, 46246966018211028668416, 1405124434459231021756179283968, 453518708737693704370173592484540645376, 1545285638496177620571506637671497728000000000000

Offset: 1

Author

Seiichi Manyama, Jan 11 2021

Keywords

• nonn

Crossrefs

Main diagonal of A340560.

Cf. A212800.

Programs

Mathematica

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 *)

PARI

default(realprecision, 120);
{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)))}

Formula

a(n) = A212800(n)/n^2.

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