A258586 Number of solid standard Young tableaux of shape [[{n}^(n+1)],[n]^n].

1, 2, 936, 1825221320, 70351928759681296000, 160978956785364112335731878007698260, 51488321677815455036453939239317069333712945710369620220, 4648889159675386017282064494039528050991187044317172798976485350954735075040045120

Offset: 0

Author

Alois P. Heinz, Nov 06 2015

Keywords

• nonn

Links

• 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

Cf. A214722, A258583.

Programs

Maple

b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
a:= n-> b([[n$(n+1)], [n]$n]):
seq(a(n), n=0..5);