A123555 Number of standard Young tableaux of type (n+1,n,n-1).
0, 2, 16, 168, 2112, 30030, 466752, 7759752, 135980416, 2485891980, 47052314400, 916847954880, 18311313000960, 373542610526280, 7761573156274560, 163893933165976200, 3510476121410184960, 76151734612882397700, 1670824967127762045600, 37036620104665392010800, 828632324276985756528000
Offset: 0
References
- For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..700
- Joerg Arndt, The a(3)=168 Young tableaux of shape [4,3,2].
- Joel B. Lewis, Pattern avoidance and RSK-like algorithms for alternating permutations and Young tableaux, arXiv:0909.4966 [math.CO], 2009-2011. [_Joel B. Lewis_, Oct 05 2009]
- Joel B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012.
- Sherry H. F. Yan, On Wilf equivalence for alternating permutations, Elect. J. Combinat.; 20 (2013), #P58.
- Index entries for sequences related to Young tableaux.
Crossrefs
Cf. A011553.
For up-down permutations of even length, see A005789. [Joel B. Lewis, Oct 05 2009]
Programs
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Mathematica
f[n_]:=16 (3 n)!/((n-1)! (n+1)! (n+3)!) (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@ {n + 1, n, n - 1}, {n, 0, 17}] (* Robert G. Wilson v *) -
PARI
for(n=0,25, print1(16*(3*n)!/((n-1)!*(n+1)!*(n+3)!), ", ")) \\ G. C. Greubel, Oct 15 2017
Formula
a(n) = 16*(3*n)!/((n-1)!*(n+1)!*(n+3)!).
(n-1)*(n+3)*(n+1)*a(n) -3*n*(3*n-1)*(3*n-2)*a(n-1)=0, n>1. - R. J. Mathar, Aug 10 2015
G.f.: 2x*3F2(5/3,4/3,2;3,5;27x). - R. J. Mathar, Aug 10 2015
Comments