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%I #8 Sep 08 2022 08:45:13
%S 1,2,96,497664,825564856320,1027134771639091200000,
%T 1932215036193527461576704000000000,
%U 9973959265081827837426668870219857920000000000000
%N Hankel transform of the sequence A001469 (unsigned), Genocchi numbers of first kind.
%C This sequence is the Hankel transform (see A001906 for definition)of the sequence defined by, for n>=0, a(n) = |A001469(n+1)|; example: det([1, 1, 3, 17; 1, 3, 17, 155; 3, 17, 155, 2073; 17, 155, 2073, 38227]) = 497664 = 4!*12^4.
%H G. C. Greubel, <a href="/A091810/b091810.txt">Table of n, a(n) for n = 0..24</a>
%F a(n) = (n+1)!*A000178(n)^4 = (n+1)!*A055209(n)^2.
%t Table[(n + 1)!*BarnesG[n + 2]^4, {n, 0, 10}] (* _G. C. Greubel_, Oct 14 2018 *)
%o (PARI) for(n=0,10, print1((n+1)!*(prod(k=0,n, (k!)^2))^2, ", ")) \\ _G. C. Greubel_, Oct 14 2018
%o (Magma) [Factorial(n+1)*(&*[(Factorial(k))^2: k in [0..n]])^2: n in [0..10]]; // _G. C. Greubel_, Oct 14 2018
%Y Cf. A000178 A001469 A001906 A055209.
%K nonn
%O 0,2
%A _Philippe Deléham_, Mar 07 2004
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