A215299 Number of solid standard Young tableaux of shape [[n,n-3],[3]].

5, 98, 962, 7020, 43573, 245962, 1305238, 6633172, 32649890, 156817044, 738717796, 3425580376, 15679951989, 70992594650, 318450985230, 1417072222020, 6261985407990, 27502477286460, 120137081521500, 522256720264680, 2260525598620770, 9746264904755652

Offset: 3

Author

Alois P. Heinz, Aug 07 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..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=3 of A214775.

Cf. A215002.

Programs

Maple

a:= proc(n) option remember; `if`(n<5, [0$2, 5, 98][n],
      2*(32*n^7 -400*n^6 +1976*n^5 -4900*n^4 +6452*n^3 -4420*n^2
      +1350*n-315)*a(n-1) / (16*n^7 -224*n^6 +1204*n^5 -3008*n^4
      +2980*n^3 +1072*n^2 -4155*n +2205))
    end:
seq(a(n), n=3..30);

Mathematica

Flatten[{5, Table[(8*(45 - 180*n + 580*n^2 - 756*n^3 + 484*n^4 - 144*n^5 + 16*n^6) * (2*n-6)!) / (3*(n-3)!*(n+1)!), {n, 4, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

Formula

See Maple program.

For n > 3, a(n) = (8*(45 - 180*n + 580*n^2 - 756*n^3 + 484*n^4 - 144*n^5 + 16*n^6) * (2*n-6)!) / (3 * (n-3)! * (n+1)!). - Vaclav Kotesovec, Sep 02 2014