%I #11 Jan 08 2021 06:41:23

%S 1,1,1,1,13,1,1,121,181,1,1,1093,18281,2521,1,1,9841,1690781,2803921,

%T 35113,1,1,88573,152963281,2732887529,430503601,489061,1,1,797161,

%U 13755675781,2555011015201,4447515497881,66102491401,6811741,1

%N Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - sin(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 1, 13, 121, 1093, 9841, ...

%e 1, 181, 18281, 1690781, 152963281, ...

%e 1, 2521, 2803921, 2732887529, 2555011015201, ...

%e 1, 35113, 430503601, 4447515497881, 43384923739812577, ...

%o (PARI) default(realprecision, 120);

%o {T(n, k) = round(4^(2*n*k)*prod(a=1, n, prod(b=1, k, 1-(sin(a*Pi/(2*n+1))*cos(b*Pi/(2*k+1)))^2)))}

%Y Main diagonal gives A340295.

%Y Cf. A340427, A340428, A340430.

%K nonn,tabl

%O 0,5

%A _Seiichi Manyama_, Jan 07 2021