A059490 Expansion of generating function A_{QT}^(1)(4n;2).

1, 1, 5, 105, 9009, 3128697, 4379132901, 24645892667825, 556965289746386625, 50494858759761851228625, 18354114596951084500741513125, 26735929307256782047733105984465625, 156023842049488378026019378718492161640625, 3646806710157227756289546514549111188854996015625

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..57

G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001 [Th. 5].

Maple

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]
# second Maple program:
a:= n-> 2^(n*(n-1))*abs(mul(mul((4*(j-i)+1)/(j-i+n), j=1..n), i=1..n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 11 2017

Mathematica

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 *)

Crossrefs

Sequence in context: A200851 A203471 A015002 * A204109 A093979 A293261

Adjacent sequences: A059487 A059488 A059489 * A059491 A059492 A059493

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 04 2001

Status

approved