%I #13 Dec 28 2022 09:04:29
%S 1,3,14,84,360,2160,10080,60480,249984,1499904,6999552,41997312,
%T 179988480,1079930880,5039677440,30238064640,122903101440,
%U 737418608640,3441286840320,20647721041920,88490233036800,530941398220800,2477726525030400,14866359150182400
%N Square root of determinant of skew-symmetric 2n X 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n.
%F It appears that for n > 1, a(n) / a(n-1) = 2 * (4*e(n)-1) / (2*e(n)-1), where e(n) = A006519(n).
%t a[0] = 1;
%t a[n_] := Sqrt@Det@Table[Sign[i - j] BitXor[i, j], {i, 2 n}, {j, 2 n}];
%t Table[a[n], {n, 0, 20}]
%o (PARI) a(n) = sqrtint(matdet(matrix(2*n, 2*n, i, j, sign(i-j)*bitxor(i,j)))); \\ _Michel Marcus_, Dec 28 2022
%Y Cf. A006519.
%K nonn
%O 0,2
%A _Andrey Zabolotskiy_, Dec 26 2022