A215298 Number of solid standard Young tableaux of shape [[n,n-2],[2]].

2, 25, 174, 962, 4804, 22689, 103510, 461318, 2021916, 8752042, 37520972, 159633060, 674969224, 2839400945, 11893509990, 49637986590, 206519808300, 856904298030, 3547095101220, 14652264350940, 60412895258040, 248675669866650, 1022088942267900, 4195255959533052

Offset: 2

Author

Alois P. Heinz, Aug 07 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..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=2 of A214775.

Cf. A215002.

Programs

Maple

a:= proc(n) option remember; `if`(n=2, 2,
      2*(4*n^5 -26*n^4 +60*n^3 -58*n^2 +22*n -5)*a(n-1)/
        (2*n^5 -14*n^4 +30*n^3 -10*n^2 -31*n +25))
    end:
seq(a(n), n=2..30);

Mathematica

Table[12*(1 - 4*n + 10*n^2 - 8*n^3 + 2*n^4) * (2*n-4)! / ((n-2)! * (n+1)!), {n, 2, 20}] (* Vaclav Kotesovec, Sep 02 2014 *)

Formula

See Maple program.

a(n) ~ 3 * 2^(2*n-1) * sqrt(n) / sqrt(Pi). - Vaclav Kotesovec, Sep 02 2014

a(n) = 12*(1 - 4*n + 10*n^2 - 8*n^3 + 2*n^4) * (2*n-4)! / ((n-2)! * (n+1)!). - Vaclav Kotesovec, Sep 02 2014