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Second series of Hankel determinants based on A001044(n+1)=((n+1)!)^2 : a(n)=det(A001044(i+j-1))=det(((i+j-1)!)^2), i,j=1,2...n. Hankel transform of A001044(n+1).
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%I #4 Feb 24 2019 07:35:08

%S 1,20,75456,222049714176,1446859308630697574400,

%T 47680530046593302430474043392000000,

%U 15747911603441625571224989926437024694272000000000000

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

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

%t nmax = 10; Table[Det[Table[((i+j-1)!)^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