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REFERENCES
| J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 17).
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MAPLE
| with(linalg): b:= proc(n) option remember; local l, ll, i, j, h0, h1, M; if n=0 then RETURN (1) fi; if n<0 or member(irem(n, 4), [1, 2]) then RETURN (0) fi; l:= []; for j from 1 to n-1 do h0:= j*(j-1)/2+1; h1:= j*(j+1)/2+1; for i from 1 to j do l:= [l[], [h1, h1+1]]; if irem (i, 2)=1 then l:= [l[], [h1, h0]]; h1:= h1+1; l:=[l[], [h1, h0]]; h0:=h0+1 else l:= [l[], [h0, h1]]; h1:= h1+1; l:=[l[], [h0, h1]]; h0:=h0+1 fi od od; M:= Matrix ((n+1)*n/2); for ll in l do M[ll[1], ll[2]]:= 1; M[ll[2], ll[1]]:= -1 od: sqrt (det (M)); end: a:= n-> b(2*n +irem (n, 2)); seq (a(n), n=0..10); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), May 08 2010]
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