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%I A340427 #18 Jan 07 2021 19:27:41
%S A340427 1,1,1,1,12,1,1,140,140,1,1,1632,17745,1632,1,1,19024,2227120,2227120,
%T A340427 19024,1,1,221760,279215849,2958176256,279215849,221760,1,1,2585024,
%U A340427 35001302700,3909096873216,3909096873216,35001302700,2585024,1
%N A340427 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * sin(b*Pi/(2*k))^2).
%F A340427 T(n,k) = T(k,n).
%F A340427 T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - cos(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).
%F A340427 T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).
%e A340427 Square array begins:
%e A340427   1,     1,         1,             1,                 1, ...
%e A340427   1,    12,       140,          1632,             19024, ...
%e A340427   1,   140,     17745,       2227120,         279215849, ...
%e A340427   1,  1632,   2227120,    2958176256,     3909096873216, ...
%e A340427   1, 19024, 279215849, 3909096873216, 54090331699622625, ...
%o A340427 (PARI) default(realprecision, 120);
%o A340427 {T(n, k) = round(4^(2*(n-1)*(k-1))*prod(a=1, n-1, prod(b=1, k-1, 1-(sin(a*Pi/(2*n))*sin(b*Pi/(2*k)))^2)))}
%Y A340427 Main diagonal gives A340166.
%Y A340427 Cf. A340425, A340428, A340430, A340432.
%K A340427 nonn,tabl
%O A340427 1,5
%A A340427 _Seiichi Manyama_, Jan 07 2021

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