A340557 - OEIS

%I #11 Mar 18 2023 05:18:04

%S 1,6,196,64152,220581904,7902001927776,2930937179395968064,

%T 11225532133258005621166464,443461906581614469808503571611904,

%U 180610519352999624076350648705004622628352

%N 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).

%F 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

%t 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 *)

%o (PARI) default(realprecision, 120);

%o {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)))}

%Y Main diagonal of A103999.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 11 2021