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Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n} Product_{b=1..k-1} (4*sin((2*a-1)*Pi/(2*n))^2 + 4*sin(2*b*Pi/k)^2) ).
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%I #13 Feb 19 2021 18:30:05

%S 1,2,1,7,2,1,16,25,2,1,41,72,112,2,1,98,361,400,529,2,1,239,1250,4961,

%T 2312,2527,2,1,576,5041,25088,77841,13456,12100,2,1,1393,18432,200999,

%U 559682,1270016,78408,57967,2,1

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

%F If k is odd, T(n,k) = A341533(n,k)/2.

%e Square array begins:

%e 1, 2, 7, 16, 41, 98, ...

%e 1, 2, 25, 72, 361, 1250, ...

%e 1, 2, 112, 400, 4961, 25088, ...

%e 1, 2, 529, 2312, 77841, 559682, ...

%e 1, 2, 2527, 13456, 1270016, 12771458, ...

%e 1, 2, 12100, 78408, 20967241, 292820000, ...

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

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

%Y Main diagonal gives A341782.

%Y Cf. A341533, A341739, A341741.

%K nonn,tabl

%O 1,2

%A _Seiichi Manyama_, Feb 18 2021