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%I #14 Sep 25 2022 22:55:50
%S 1,1,5,105,9009,3128697,4379132901,24645892667825,556965289746386625,
%T 50494858759761851228625,18354114596951084500741513125,
%U 26735929307256782047733105984465625,156023842049488378026019378718492161640625,3646806710157227756289546514549111188854996015625
%N Expansion of generating function A_{QT}^(1)(4n;2).
%H G. C. Greubel, <a href="/A059490/b059490.txt">Table of n, a(n) for n = 0..57</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].
%p A059490 := proc(n) local i, j, t1; t1 := (-1)^(n*(n-1)/2)*2^(n^2-n); for i to n do for j to n do t1 := t1*(4*j - 4*i + 1)/(j - i + n); end do end do; t1 end proc; # [Corrected by _Sean A. Irvine_, Sep 25 2022]
%p # second Maple program:
%p a:= n-> 2^(n*(n-1))*abs(mul(mul((4*(j-i)+1)/(j-i+n), j=1..n), i=1..n)):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 11 2017
%t a[n_] := (-1)^(n*(n - 1)/2)*2^(n*(n - 1))*Product[Product[(4*(j - i) + 1)/(j - i + n), {i, 0, n - 1}], {j, 0, n - 1}]; Table[a[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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