A059491 Expansion of generating function A_{QT}^(1)(4n;3).
1, 1, 6, 189, 30618, 25332021, 106698472452, 2283997201168644, 248218139523497121576, 136861610819571430116630660, 382684747771430768732371981946100, 5424628155237728987530088501811168904125, 389729317367139375014273384868937660572301897500
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..50
- G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001 [Th. 5].
Programs
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Mathematica
f[n_] := Product[(3 k + 1)!/(n + k)!, {k, 0, n - 1}]; Table[3^(n*(n - 1)/2)*f[n], {n,0,20}] (* G. C. Greubel, Sep 10 2017 *)
Formula
a(n) = 3^(n*(n-1)/2)*A005130(n).
a(n+1) is the Hankel transform of A097188. Odd terms occur in a(n+1) at positions given by 2*A000975(n). - Paul Barry, Feb 09 2007