A215123 Number of solid standard Young tableaux of shape [[n^2,n],[n]].

1, 2, 174, 52808, 31497284, 31113230148, 46190668836656, 96484621769643360, 270280816277448460968, 979042561410295182717884, 4456728497956906393963534248, 24916868994347706845906490576432, 167903137478620963997932010166057408

Offset: 0

Author

Alois P. Heinz, Aug 03 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100
• 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

Central row elements of A215122.

Main diagonal of A176129.

Programs

Maple

b:= proc(x, y, z) option remember; `if`(zy and x>z, b(x-1, y, z), 0)+
      `if`(y>0, b(x, y-1, z), 0)+ `if`(z>0, b(x, y, z-1), 0)))
    end:
a:= n-> b(n^2, n, n):
seq(a(n), n=0..15);

Mathematica

$RecursionLimit = 1000; b[x_, y_, z_] :=  b[x, y, z] = If[zy && x>z, b[x-1, y, z], 0] + If[y>0, b[x, y-1, z], 0] + If[z>0, b[x, y, z-1], 0]]]; a[n_] := b[n^2, n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)

Formula

a(n) ~ exp(2*n+2) * n^(2*n-1) / (2*Pi). - Vaclav Kotesovec, Jan 19 2015