cp's OEIS Frontend

A340428 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - sin(a*Pi/(2*n+1))^2 * sin(b*Pi/(2*k+1))^2).

%I A340428 #15 Jan 08 2021 06:41:37
%S A340428 1,1,1,1,7,1,1,61,61,1,1,547,4961,547,1,1,4921,432461,432461,4921,1,1,
%T A340428 44287,38484961,371647151,38484961,44287,1,1,398581,3445022461,
%U A340428 330435708793,330435708793,3445022461,398581,1
%N A340428 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - sin(a*Pi/(2*n+1))^2 * sin(b*Pi/(2*k+1))^2).
%F A340428 T(n,k) = T(k,n).
%e A340428 Square array begins:
%e A340428   1,    1,        1,            1,                1, ...
%e A340428   1,    7,       61,          547,             4921, ...
%e A340428   1,   61,     4961,       432461,         38484961, ...
%e A340428   1,  547,   432461,    371647151,     330435708793, ...
%e A340428   1, 4921, 38484961, 330435708793, 2952717950351617, ...
%o A340428 (PARI) default(realprecision, 120);
%o A340428 {T(n, k) = round(4^(2*n*k)*prod(a=1, n, prod(b=1, k, 1-(sin(a*Pi/(2*n+1))*sin(b*Pi/(2*k+1)))^2)))}
%Y A340428 Main diagonal gives A340292.
%Y A340428 Cf. A340427, A340430, A340432.
%K A340428 nonn,tabl
%O A340428 0,5
%A A340428 _Seiichi Manyama_, Jan 07 2021