A215220 Number of solid standard Young tableaux of shape [[n,n,n,n],[n]].

1, 4, 456, 143164, 75965484, 55824699632, 51274161733160, 55418842406649988, 67819708829687672202, 91539069926354814114556, 133752944758581353219955762, 208673064320580765981337783096, 343997162091593719562479905281938, 594344377404793356460064021706935470

Offset: 0

Author

Alois P. Heinz, Aug 06 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..40
• 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 A214722.

Programs

Maple

b:= proc(w, x, y, z, u) option remember;
     `if`({w, x, y, z, u}={0}, 1, `if`(w>x and w>u, b(w-1, x, y, z, u), 0)+
     `if`(x>y, b(w, x-1, y, z, u), 0)+ `if`(y>z, b(w, x, y-1, z, u), 0)+
     `if`(z>0, b(w, x, y, z-1, u), 0)+ `if`(u>0, b(w, x, y, z, u-1), 0))
    end:
a:= n-> b(n$5):
seq(a(n), n=0..20);

Mathematica

b[w_, x_, y_, z_, u_] := b[w, x, y, z, u] =
  If[Union@{w, x, y, z, u} == {0}, 1,
  If[w > x && w > u, b[w - 1, x, y, z, u], 0] +
  If[x > y, b[w, x - 1, y, z, u], 0] +
  If[y > z, b[w, x, y - 1, z, u], 0] +
  If[z > 0, b[w, x, y, z - 1, u], 0] +
  If[u > 0, b[w, x, y, z, u - 1], 0]];
a[n_] :=  b[n, n, n, n, n];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 08 2017, translated from Maple *)