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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).
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%I #17 Feb 19 2021 18:30:12

%S 1,1,8,1,36,49,1,200,625,288,1,1156,12544,9216,1681,1,6728,279841,

%T 583200,130321,9800,1,39204,6385729,44408896,24611521,1822500,57121,1,

%U 228488,146410000,3546167328,6059221281,1003520000,25411681,332928

%N 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).

%e Square array begins:

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

%e 8, 36, 200, 1156, 6728, ...

%e 49, 625, 12544, 279841, 6385729, ...

%e 288, 9216, 583200, 44408896, 3546167328, ...

%e 1681, 130321, 24611521, 6059221281, 1612940640256, ...

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

%o 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)));

%Y Main diagonal gives A341478(n)^2.

%Y Cf. A341533, A341738, A341741.

%K nonn,tabl

%O 1,3

%A _Seiichi Manyama_, Feb 18 2021