A340561 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*cos(b*Pi/k)^2) ).

1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 12, 16, 4, 1, 1, 29, 75, 45, 5, 1, 1, 70, 361, 384, 121, 6, 1, 1, 169, 1728, 3509, 1805, 320, 7, 1, 1, 408, 8281, 31500, 30976, 8100, 841, 8, 1, 1, 985, 39675, 284089, 508805, 261725, 35287, 2205, 9, 1

Offset: 1

Author

Seiichi Manyama, Jan 11 2021

Keywords

• nonn
• tabl

Examples

			Square array begins:
  1, 1,   1,    1,      1,       1, ...
  1, 2,   5,   12,     29,      70, ...
  1, 3,  16,   75,    361,    1728, ...
  1, 4,  45,  384,   3509,   31500, ...
  1, 5, 121, 1805,  30976,  508805, ...
  1, 6, 320, 8100, 261725, 7741440, ...
		

Crossrefs

Columns 1..4 give A000012, A000027, A004146, A006235.

Rows 1..3 give A000012, A000129, A005386.

Main diagonal gives A340563.

T(n, 2*n) gives A252767.

Cf. A173958, A340476, A340560.

Programs

PARI

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