%I #8 Sep 27 2024 05:44:44
%S 1,-4,144,-43264,106832896,-2155963622400,354617391605760000,
%T -474686810341051524710400,5166329306435680284163452174336,
%U -456900249341808231214942590547243565056
%N Hankel transform of A138175.
%C When aerated, gives Hankel transform of A138175.
%H A. V. Razumov and Yu. G. Stroganov, <a href="https://arxiv.org/abs/math-ph/0312071">On refined enumerations of some symmetry classes of alternating sign matrices</a>, arXiv:math-ph/0312071, 2003.
%F sqrt(abs(a(n)))/2^n = A005156(n).
%F a(n) = (-1)^n*(Product_{k=1..n} (6*k-2)!*(2*k-1)!/((4*k-1)!*(4*k-2)!))^2.
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 03 2008