A341739 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} (4*sin(a*Pi/n)^2 + 4*sin((2*b-1)*Pi/(2*k))^2).

1, 1, 8, 1, 36, 49, 1, 200, 625, 288, 1, 1156, 12544, 9216, 1681, 1, 6728, 279841, 583200, 130321, 9800, 1, 39204, 6385729, 44408896, 24611521, 1822500, 57121, 1, 228488, 146410000, 3546167328, 6059221281, 1003520000, 25411681, 332928

Offset: 1

Author

Seiichi Manyama, Feb 18 2021

Keywords

• nonn
• tabl

Examples

			Square array begins:
     1,      1,        1,          1,             1, ...
     8,     36,      200,       1156,          6728, ...
    49,    625,    12544,     279841,       6385729, ...
   288,   9216,   583200,   44408896,    3546167328, ...
  1681, 130321, 24611521, 6059221281, 1612940640256, ...
		

Crossrefs

Main diagonal gives A341478(n)^2.

Cf. A341533, A341738, A341741.

Programs

PARI

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