cp's OEIS Frontend

A340561 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*cos(b*Pi/k)^2) ).

%I A340561 #25 Jan 13 2021 01:28:11
%S A340561 1,1,1,1,2,1,1,5,3,1,1,12,16,4,1,1,29,75,45,5,1,1,70,361,384,121,6,1,
%T A340561 1,169,1728,3509,1805,320,7,1,1,408,8281,31500,30976,8100,841,8,1,1,
%U A340561 985,39675,284089,508805,261725,35287,2205,9,1
%N A340561 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*cos(b*Pi/k)^2) ).
%e A340561 Square array begins:
%e A340561   1, 1,   1,    1,      1,       1, ...
%e A340561   1, 2,   5,   12,     29,      70, ...
%e A340561   1, 3,  16,   75,    361,    1728, ...
%e A340561   1, 4,  45,  384,   3509,   31500, ...
%e A340561   1, 5, 121, 1805,  30976,  508805, ...
%e A340561   1, 6, 320, 8100, 261725, 7741440, ...
%o A340561 (PARI) default(realprecision, 120);
%o A340561 {T(n, k) = round(sqrt(prod(a=1, n-1, prod(b=1, k-1, 4*sin(a*Pi/n)^2+4*cos(b*Pi/k)^2))))}
%Y A340561 Columns 1..4 give A000012, A000027, A004146, A006235.
%Y A340561 Rows 1..3 give A000012, A000129, A005386.
%Y A340561 Main diagonal gives A340563.
%Y A340561 T(n, 2*n) gives A252767.
%Y A340561 Cf. A173958, A340476, A340560.
%K A340561 nonn,tabl
%O A340561 1,5
%A A340561 _Seiichi Manyama_, Jan 11 2021