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First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A001044.
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%I #8 Feb 24 2019 07:35:02

%S 1,3,656,58910976,7213311014731776,3024546589156405495726080000,

%T 9172616430046109813423337553212211200000000

%N First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A001044.

%C It would be highly desirable to obtain a closed form for a(n).

%t nmax = 15; Table[Det[Table[((i+j-2)!)^2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Feb 24 2019 *)

%K nonn

%O 0,2

%A _Karol A. Penson_, Sep 15 2009