A340557 a(n) = Product_{1<=j,k<=n} (4*sin(Pi*(4*j-1)/(4*n))^2 + 4*sin(Pi*(2*k-1)/(2*n))^2).

1, 6, 196, 64152, 220581904, 7902001927776, 2930937179395968064, 11225532133258005621166464, 443461906581614469808503571611904, 180610519352999624076350648705004622628352

Offset: 0

Author

Seiichi Manyama, Jan 11 2021

Keywords

• nonn

Crossrefs

Main diagonal of A103999.

Programs

Mathematica

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

PARI

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

Formula

a(n) ~ 2^(1/8) * sqrt(1 + sqrt(2)) * exp(4*G*n^2/Pi), where G is Catalan's constant A006752. - Vaclav Kotesovec, Mar 18 2023