A059491 Expansion of generating function A_{QT}^(1)(4n;3).

1, 1, 6, 189, 30618, 25332021, 106698472452, 2283997201168644, 248218139523497121576, 136861610819571430116630660, 382684747771430768732371981946100, 5424628155237728987530088501811168904125, 389729317367139375014273384868937660572301897500

Offset

0,3

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].

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

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 *)

Crossrefs

Sequence in context: A324094 A129046 A222016 * A024279 A350873 A182788

Adjacent sequences: A059488 A059489 A059490 * A059492 A059493 A059494

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 04 2001

Status

approved