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%I #10 Sep 11 2017 02:36:49
%S 1,1,6,189,30618,25332021,106698472452,2283997201168644,
%T 248218139523497121576,136861610819571430116630660,
%U 382684747771430768732371981946100,5424628155237728987530088501811168904125,389729317367139375014273384868937660572301897500
%N Expansion of generating function A_{QT}^(1)(4n;3).
%H G. C. Greubel, <a href="/A059491/b059491.txt">Table of n, a(n) for n = 0..50</a>
%H G. Kuperberg, <a href="https://arxiv.org/abs/math/0008184">Symmetry classes of alternating-sign matrices under one roof</a>, arXiv:math/0008184 [math.CO], 2000-2001 [Th. 5].
%F a(n) = 3^(n*(n-1)/2)*A005130(n).
%F a(n+1) is the Hankel transform of A097188. Odd terms occur in a(n+1) at positions given by 2*A000975(n). - _Paul Barry_, Feb 09 2007
%t f[n_] := Product[(3 k + 1)!/(n + k)!, {k, 0, n - 1}]; Table[3^(n*(n - 1)/2)*f[n], {n,0,20}] (* _G. C. Greubel_, Sep 10 2017 *)
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Feb 04 2001
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