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%I #18 Jan 03 2021 23:22:07
%S 1,1,4,96,18432,35389440,815372697600,263006617337856000,
%T 1357366631815981301760000,126095668058466123464363212800000,
%U 234278891648287676839670388023623680000000
%N a(n) = 2^(n(n-1)/2) * Product_{k=1..n} k!.
%C Equals the absolute values of the row sums of A156921. - _Johannes W. Meijer_, Feb 20 2009
%H C. Radoux, <a href="http://www.mat.univie.ac.at/~slc/opapers/s28radoux.html">Déterminants de Hankel et théorème de Sylvester</a>, Séminaire Lotharingien de Combinatoire, B28b (1992), 9 pp.
%F a(n) = 2^(n(n-1)/2) * Product_{k=1..n} k!.
%F a(n) = A006125(n) * A000178(n).
%F a(n) ~ 2^(n^2/2 + 1/2)*exp(-3*n^2/4 - n + 1/12)*n^(n^2/2 + n + 5/12)*Pi^(n/2 + 1/2)/A, where A is the Glaisher-Kinkelin constant (A074962). - _Ilya Gutkovskiy_, Dec 11 2016
%p A098695 := proc(n): 2^(n*(n-1)/2) * product(k!, k=1..n) end: seq(A098695(n), n=0..10); # _Johannes W. Meijer_, Nov 22 2012
%o (PARI) a(n) = 2^(n*(n-1)/2) * prod(k=1, n, k!); \\ _Michel Marcus_, Dec 11 2016
%K nonn
%O 0,3
%A _Ralf Stephan_, Sep 22 2004
%E a(0)=1 added, offset changed, and edited by _Johannes W. Meijer_, Feb 23 2009, Nov 22 2012
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