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A340560 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-1} (4*sin(a*Pi/n)^2 + 4*sin(b*Pi/k)^2).

%I A340560 #12 Jan 11 2021 13:51:23
%S A340560 1,1,1,1,8,1,1,49,49,1,1,288,1296,288,1,1,1681,30625,30625,1681,1,1,
%T A340560 9800,707281,2654208,707281,9800,1,1,57121,16257024,219069601,
%U A340560 219069601,16257024,57121,1,1,332928,373301041,17860500000,62500000000,17860500000,373301041,332928,1
%N A340560 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-1} (4*sin(a*Pi/n)^2 + 4*sin(b*Pi/k)^2).
%F A340560 T(n,k) = T(k,n).
%F A340560 T(n,k) = A212796(n,k)/(n*k).
%e A340560 Square array begins:
%e A340560   1,    1,      1,         1,           1, ...
%e A340560   1,    8,     49,       288,        1681, ...
%e A340560   1,   49,   1296,     30625,      707281, ...
%e A340560   1,  288,  30625,   2654208,   219069601, ...
%e A340560   1, 1681, 707281, 219069601, 62500000000, ...
%o A340560 (PARI) default(realprecision, 120);
%o A340560 {T(n, k) = round(prod(a=1, n-1, prod(b=1, k-1, 4*sin(a*Pi/n)^2+4*sin(b*Pi/k)^2)))}
%Y A340560 Rows and columns 1..2 give A000012, A001108.
%Y A340560 Main diagonal gives A340562.
%Y A340560 Cf. A212796, A340475, A340561.
%K A340560 nonn,tabl
%O A340560 1,5
%A A340560 _Seiichi Manyama_, Jan 11 2021