A340167 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 + sin(i*Pi/(2*n))^2 * sin(j*Pi/(2*n))^2).

1, 20, 153425, 450075709440, 504979178328238519521, 216703205118496785026106198144000, 35568160616301682717925992221900586646216066081, 2232861039051291914755952483706805051795013026559178904468193280

Offset: 1

Author

Seiichi Manyama, Dec 30 2020

Keywords

• nonn

Crossrefs

Cf. A340165, A340166.

Programs

Mathematica

Table[4^(2*(n-1)^2) * Product[Product[1 + Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, n-1}], {j, 1, n-1}], {n, 1, 10}] // Round (* Vaclav Kotesovec, Dec 31 2020 *)

PARI

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

Formula

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

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

a(n) ~ 2^(4*n^2 - 6*n + 17/4) * (sqrt(2) - 1)^(2*n) * exp(4*A340350*n^2/Pi^2). - Vaclav Kotesovec, Jan 05 2021