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%I #16 Jan 09 2021 07:36:36
%S 1,1,1,1,6,1,1,29,29,1,1,139,500,139,1,1,666,8329,8329,666,1,1,3191,
%T 138301,463736,138301,3191,1,1,15289,2295701,25543057,25543057,
%U 2295701,15289,1,1,73254,38105729,1404312491,4614756624,1404312491,38105729,73254,1
%N Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Product_{a=1..n} Product_{b=1..k} (4*sin(a*Pi/(2*n+1))^2 + 4*sin(b*Pi/(2*k+1))^2).
%F T(n,k) = T(k,n).
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 1, 6, 29, 139, 666, ...
%e 1, 29, 500, 8329, 138301, ...
%e 1, 139, 8329, 463736, 25543057, ...
%e 1, 666, 138301, 25543057, 4614756624, ...
%o (PARI) default(realprecision, 120);
%o {T(n, k) = round(prod(a=1, n, prod(b=1, k, 4*sin(a*Pi/(2*n+1))^2+4*sin(b*Pi/(2*k+1))^2)))}
%Y Rows and columns 0..1 give A000012, A030221.
%Y Main diagonal gives A127605.
%Y Cf. A116469, A187617, A340476.
%K nonn,tabl
%O 0,5
%A _Seiichi Manyama_, Jan 09 2021
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