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

1,2

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.

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

Maple

a:= n-> 6 *(3*n-2)! / (n! *(n-1)! *(n+2)!):
seq(a(n), n=1..25); # Alois P. Heinz, Apr 11 2012

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@{n, n - 1, n - 1}, {n, 18}]

Crossrefs

Cf. A005789, A123555, subdiagonal of A065077.

Sequence in context: A114469 A097690 A037967 * A087918 A088926 A291743

Adjacent sequences: A123688 A123689 A123690 * A123692 A123693 A123694

Keyword

nonn,easy

Author

Robert G. Wilson v, Nov 15 2006

Status

approved