A340560 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*sin(b*Pi/k)^2).

1, 1, 1, 1, 8, 1, 1, 49, 49, 1, 1, 288, 1296, 288, 1, 1, 1681, 30625, 30625, 1681, 1, 1, 9800, 707281, 2654208, 707281, 9800, 1, 1, 57121, 16257024, 219069601, 219069601, 16257024, 57121, 1, 1, 332928, 373301041, 17860500000, 62500000000, 17860500000, 373301041, 332928, 1

Offset: 1

Author

Seiichi Manyama, Jan 11 2021

Keywords

• nonn
• tabl

Examples

			Square array begins:
  1,    1,      1,         1,           1, ...
  1,    8,     49,       288,        1681, ...
  1,   49,   1296,     30625,      707281, ...
  1,  288,  30625,   2654208,   219069601, ...
  1, 1681, 707281, 219069601, 62500000000, ...
		

Crossrefs

Rows and columns 1..2 give A000012, A001108.

Main diagonal gives A340562.

Cf. A212796, A340475, A340561.

Programs

PARI

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

Formula

T(n,k) = T(k,n).

T(n,k) = A212796(n,k)/(n*k).