A215300 Number of solid standard Young tableaux of shape [[n,n-4],[4]].

14, 378, 4804, 43573, 325590, 2149454, 13054108, 74688594, 408634828, 2159302420, 11097147528, 55747502501, 274790652518, 1332928973766, 6377276361900, 30149660760870, 141057202034340, 653892592144620, 3006490865152440, 13722387184879650, 62220533305358076

Offset: 4

Author

Alois P. Heinz, Aug 07 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..500
• S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
• Wikipedia, Young tableau

Crossrefs

Column k=4 of A214775.

Cf. A215002.

Programs

Maple

a:= proc(n) option remember; `if`(n<6, [0$3, 14, 378, 4804][n],
      ((-460961029024*n^4 [phone]*n^3 -347074341314956*n^2
       [phone]*n [phone]) *a(n-1) +(104238656896016*n^4
       -2317913124589048*n^3 +16535317231755832*n^2 -44274446438628908*n
       +29901662719961532)*a(n-2) +(-391233321452352*n^4
       +7447800734464704*n^3 -48294258553516272*n^2 +122447135865649584*n
       -105955729051546080)*a(n-3)) / (286655151052*n^4 -1210962058579*n^3
       [phone]*n^2 -24951473774234*n -30771740340558))
    end:
seq(a(n), n=4..30);

Mathematica

Flatten[{14,Table[(2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567+2394*n-8862*n^2+15592*n^3-15484*n^4+9152*n^5-3292*n^6+704*n^7-82*n^8+4*n^9)),{n,5,20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

Formula

See Maple program.

For n > 4, a(n) = (2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567 + 2394*n - 8862*n^2 + 15592*n^3 - 15484*n^4 + 9152*n^5 - 3292*n^6 + 704*n^7 - 82*n^8 + 4*n^9)). - Vaclav Kotesovec, Sep 02 2014