cp's OEIS Frontend

A340475 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Product_{a=1..n} Product_{b=1..k} (4*sin(a*Pi/(2*n+1))^2 + 4*sin(b*Pi/(2*k+1))^2).

%I A340475 #16 Jan 09 2021 07:36:36
%S A340475 1,1,1,1,6,1,1,29,29,1,1,139,500,139,1,1,666,8329,8329,666,1,1,3191,
%T A340475 138301,463736,138301,3191,1,1,15289,2295701,25543057,25543057,
%U A340475 2295701,15289,1,1,73254,38105729,1404312491,4614756624,1404312491,38105729,73254,1
%N A340475 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Product_{a=1..n} Product_{b=1..k} (4*sin(a*Pi/(2*n+1))^2 + 4*sin(b*Pi/(2*k+1))^2).
%F A340475 T(n,k) = T(k,n).
%e A340475 Square array begins:
%e A340475   1,   1,      1,        1,          1, ...
%e A340475   1,   6,     29,      139,        666, ...
%e A340475   1,  29,    500,     8329,     138301, ...
%e A340475   1, 139,   8329,   463736,   25543057, ...
%e A340475   1, 666, 138301, 25543057, 4614756624, ...
%o A340475 (PARI) default(realprecision, 120);
%o A340475 {T(n, k) = round(prod(a=1, n, prod(b=1, k, 4*sin(a*Pi/(2*n+1))^2+4*sin(b*Pi/(2*k+1))^2)))}
%Y A340475 Rows and columns 0..1 give A000012, A030221.
%Y A340475 Main diagonal gives A127605.
%Y A340475 Cf. A116469, A187617, A340476.
%K A340475 nonn,tabl
%O A340475 0,5
%A A340475 _Seiichi Manyama_, Jan 09 2021