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%I #32 Jul 22 2023 12:39:13
%S 1,3,21,210,2574,36036,554268,9145422,159352050,2900207310,
%T 54698315490,1062710129520,21172455657360,431010704453400,
%U 8939669081780520,188478023140872630,4031562420682009290,87350519114776867950,1914486941500560677250,42397183540866961907100
%N a(n) = number of standard Young tableaux of type (n,n-1,n-1).
%H Alois P. Heinz, <a href="/A123691/b123691.txt">Table of n, a(n) for n = 1..700</a>
%H Wolfgang Unger, <a href="http://arxiv.org/abs/1411.4493">Combinatorics of Lattice QCD at Strong Coupling</a>, arXiv:1411.4493 [hep-lat], 2014.
%F a(n) = 6*(3*n-2)! / (n!*(n-1)!*(n+2)!). - _Alois P. Heinz_, Apr 11 2012
%F n*(n+2)*a(n) - 3*(3*n-2)*(3*n-4)*a(n-1) = 0. - _R. J. Mathar_, Aug 10 2015
%F G.f.: x*3F2(1,2/3,4/3;2,4;27x). - _R. J. Mathar_, Aug 10 2015
%p a:= n-> 6 *(3*n-2)! / (n! *(n-1)! *(n+2)!):
%p seq(a(n), n=1..25); # _Alois P. Heinz_, Apr 11 2012
%t (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@{n, n - 1, n - 1}, {n, 18}]
%Y Cf. A005789, A123555, subdiagonal of A065077.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Nov 15 2006
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