A340181 a(n) = Product_{1<=j,k,m<=n} (4*sin(j*Pi/(2*n+1))^2 + 4*sin(k*Pi/(2*n+1))^2 + 4*sin(m*Pi/(2*n+1))^2).

1, 9, 7486875, 14334918272193811385583, 1483160703050490588200236172057973908184332257091136

Offset: 0

Author

Seiichi Manyama, Dec 31 2020

Keywords

• nonn

Comments

(a(n)/((2n + 1)*3^n))^(1/3) is an integer.

Crossrefs

Cf. A124647, A127605, A340182, A340183.

Programs

Mathematica

Round[Table[2^(n^3)* Product[3 - Cos[2*j*Pi/(2*n + 1)] - Cos[2*k*Pi/(2*n + 1)] - Cos[2*m*Pi/(2*n + 1)], {j, 1, n}, {k, 1, n}, {m, 1, n}], {n, 0, 5}]] (* Vaclav Kotesovec, Jan 04 2021 *)

PARI

default(realprecision, 500);
{a(n) = round(prod(j=1, n, prod(k=1, n, prod(m=1, n, 4*sin(j*Pi/(2*n+1))^2+4*sin(k*Pi/(2*n+1))^2+4*sin(m*Pi/(2*n+1))^2))))}

Formula

Limit_{n->infinity} a(n)^(1/n^3) = exp(8*A340322/Pi^3). - Vaclav Kotesovec, Jan 05 2021