A123691 a(n) = number of standard Young tableaux of type (n,n-1,n-1).
1, 3, 21, 210, 2574, 36036, 554268, 9145422, 159352050, 2900207310, 54698315490, 1062710129520, 21172455657360, 431010704453400, 8939669081780520, 188478023140872630, 4031562420682009290, 87350519114776867950, 1914486941500560677250, 42397183540866961907100
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..700
- Wolfgang Unger, Combinatorics of Lattice QCD at Strong Coupling, arXiv:1411.4493 [hep-lat], 2014.
Programs
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Maple
a:= n-> 6 *(3*n-2)! / (n! *(n-1)! *(n+2)!): seq(a(n), n=1..25); # Alois P. Heinz, Apr 11 2012
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Mathematica
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@{n, n - 1, n - 1}, {n, 18}]
Formula
a(n) = 6*(3*n-2)! / (n!*(n-1)!*(n+2)!). - Alois P. Heinz, Apr 11 2012
n*(n+2)*a(n) - 3*(3*n-2)*(3*n-4)*a(n-1) = 0. - R. J. Mathar, Aug 10 2015
G.f.: x*3F2(1,2/3,4/3;2,4;27x). - R. J. Mathar, Aug 10 2015