A215124 Number of solid standard Young tableaux of shape [[(n-2)*2,2],[n-2]].

0, 0, 0, 8, 174, 2084, 21025, 194064, 1694224, 14232672, 116228871, 928763000, 7294771770, 56497996620, 432520209420, 3278863236544, 24649138276800, 183964353480832, 1364323157872947, 10061883449658936, 73839952091271730, 539488089621673500

Offset: 0

Author

Alois P. Heinz, Aug 03 2012

Keywords

• nonn

Comments

a(n) is odd if and only if n = 2*k and k >= 3 and k in { A118113 }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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=2 of A215122.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, [0, 0, 0, 8][n+1],
      3*(n-1)*(3*n-8)*(3*n-10)*(937*n-486*n^2+81*n^3-576)*a(n-1)
      /(2*(n-2)^2*(2*n-3)*(2152*n-729*n^2+81*n^3-2080)))
    end:
seq(a(n), n=0..30);

Mathematica

Flatten[{0, 0, 0, 8, Table[3*(n-1) * (3*n-8) * (-576 + 937*n - 486*n^2 + 81*n^3) * (3*n-10)! / (2 * (n-4)! * (2*n-3)!), {n, 4, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

Formula

For n > 3, a(n) = 3*(n-1) * (3*n-8) * (-576 + 937*n - 486*n^2 + 81*n^3) * (3*n-10)! / (2 * (n-4)! * (2*n-3)!). - Vaclav Kotesovec, Sep 02 2014