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%I #15 Jul 05 2021 16:52:54
%S 1,4,2304,1194393600,1941728542064640000,
%T 25569049282962188245401600000000,
%U 5866627428836325123819714259080708096000000000000
%N a(n) = Product_{i=0..n-1} ((2i)!)^2.
%C a(n) = determinant of n X n matrix m(i,j)=E(2i+2j), 0<=i,j<=n-1, where E(2k) is the (2k)-th signless Euler number in 1/cos(z) = Sum_{k>=0} E(2k)*z^(2k)/(2k)!.
%D C. Krattenthaler, Advanced Determinant Calculus, p. 46
%H C. Krattenthaler, <a href="http://www.mat.univie.ac.at/~kratt/artikel/detsurv.html">Advanced Determinant Calculus</a>, Séminaire Lotharingien Combin. 42 ("The Andrews Festschrift") (1999), Article B42q, 67 pp.
%t Table[Product[((2i)!)^2,{i,0,n-1}],{n,8}] (* _Harvey P. Dale_, Jul 05 2021 *)
%o (PARI) a(n)=prod(i=0,n-1,((2*i)!)^2)
%K nonn
%O 1,2
%A _Benoit Cloitre_, Sep 18 2004
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