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A057170 2-enumeration of 2n X 2n half-turn symmetric alternating-sign matrices. 1

%I

%S 1,2,12,288,26880,10035200,14836039680,87734404251648,

%T 2064716402685640704,194361783607326689722368,

%U 72958995691997968023051829248,109548594452892660460226753134067712,656593430123179564638165745256190909087744,15741504841171021653720624575980053578961033101312

%N 2-enumeration of 2n X 2n half-turn symmetric alternating-sign matrices.

%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. 3].

%p A057170 := proc(n) local i, j, t1; t1 := 2^(n^2); for i to n do for j to n do if j-i mod 2 <> 0 then t1 := t1*(2*j - 2*i + 1)/(2*j - 2*i) end if end do end do; t1 end proc;

%t a[n_] := Module[{t1 = 2^(n^2)}, Do[If[OddQ[j-i], t1 = t1*(2*j - 2*i + 1) / (2*j - 2*i)], {j, n}, {i, n}]; t1];

%t Array[a, 14, 0] (* _Jean-Fran├žois Alcover_, Nov 28 2017, from Maple *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Feb 04 2001

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)