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

1, 2, 12, 288, 26880, 10035200, 14836039680, 87734404251648, 2064716402685640704, 194361783607326689722368, 72958995691997968023051829248, 109548594452892660460226753134067712, 656593430123179564638165745256190909087744, 15741504841171021653720624575980053578961033101312

Offset

0,2

Links

Table of n, a(n) for n=0..13.

G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001; [Th. 3].

Maple

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;

Mathematica

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];
Array[a, 14, 0] (* Jean-François Alcover, Nov 28 2017, from Maple *)

Crossrefs

Sequence in context: A003121 A211937 A176037 * A200564 A008338 A000178

Adjacent sequences: A057167 A057168 A057169 * A057171 A057172 A057173

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 04 2001

Status

approved