A341478 a(n) = sqrt( Product_{1<=j<=n-1} Product_{1<=k<=n} (4*sin(j*Pi/n)^2 + 4*sin((2*k-1)*Pi/(2*n))^2) ).

1, 1, 6, 112, 6664, 1270016, 776239200, 1522266730496, 9580300901941376, 193509323594243571712, 12545297912843041612924416, 2610531939025273190037188509696, 1743627211475190637398673259679582208

Offset: 0

Author

Seiichi Manyama, Feb 13 2021

Keywords

• nonn

Crossrefs

Cf. A335586, A340562, A341479, A341493.

Programs

Mathematica

Table[Sqrt[Product[4*Sin[j*Pi/n]^2 + 4*Sin[(2*k - 1)*Pi/(2*n)]^2, {k, 1, n}, {j, 1, n-1}]], {n, 0, 15}] // Round (* Vaclav Kotesovec, Feb 14 2021 *)

PARI

default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n-1, prod(k=1, n, 4*sin(j*Pi/n)^2+4*sin((2*k-1)*Pi/(2*n))^2))));

Formula

a(n) ~ exp(2*G*n^2/Pi) / 2^(3/4), where G is Catalan's constant A006752. - Vaclav Kotesovec, Feb 14 2021