A341782 a(n) = sqrt( Product_{j=1..n} Product_{k=1..n-1} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin(2*k*Pi/n)^2) ).

1, 1, 2, 112, 2312, 1270016, 292820000, 1522266730496, 3772667519238272, 193509323594243571712, 5041011532336819845120512, 2610531939025273190037188509696

Offset: 0

Author

Seiichi Manyama, Feb 19 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..62

Crossrefs

Main diagonal of A341738.

Cf. A341478, A341535.

Programs

Mathematica

Table[Sqrt[Product[Product[(4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[2*k*Pi/n]^2), {j, 1, n}], {k, 1, n - 1}]], {n, 0, 15}] // Round (* Vaclav Kotesovec, Mar 18 2023 *)

PARI

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

Formula

If n is odd, a(n) = A341535(n)/2.

If n is odd, a(n) = A341478(n).

a(n) ~ exp(2*G*n^2/Pi) / (2^(3/4) * (1 + (1 + (-1)^n)/sqrt(2))), where G is Catalan's constant A006752. - Vaclav Kotesovec, Mar 18 2023