cp's OEIS Frontend

A340430 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 - cos(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).

%I A340430 #13 Jan 08 2021 06:42:05
%S A340430 1,1,1,1,15,1,1,209,209,1,1,2911,32625,2911,1,1,40545,5015009,5015009,
%T A340430 40545,1,1,564719,770100001,8238791743,770100001,564719,1,1,7865521,
%U A340430 118247646001,13441754883649,13441754883649,118247646001,7865521,1
%N A340430 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 - cos(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).
%F A340430 T(n,k) = T(k,n).
%e A340430 Square array begins:
%e A340430   1,     1,         1,              1,                  1, ...
%e A340430   1,    15,       209,           2911,              40545, ...
%e A340430   1,   209,     32625,        5015009,          770100001, ...
%e A340430   1,  2911,   5015009,     8238791743,     13441754883649, ...
%e A340430   1, 40545, 770100001, 13441754883649, 230629380093001665, ...
%o A340430 (PARI) default(realprecision, 120);
%o A340430 {T(n, k) = round(4^(2*n*k)*prod(a=1, n, prod(b=1, k, 1-(cos(a*Pi/(2*n+1))*cos(b*Pi/(2*k+1)))^2)))}
%Y A340430 Main diagonal gives A340291.
%Y A340430 Cf. A340427, A340428, A340432.
%K A340430 nonn,tabl
%O A340430 0,5
%A A340430 _Seiichi Manyama_, Jan 07 2021