A258583 Number of solid standard Young tableaux of shape [[{n}^n],[n]].

1, 1, 16, 5471, 75965484, 70692556053053, 6614511157454872712100, 87353366195666890516586545068535, 217757982462900115559339884671224174403391534, 132100470099008733697710444705793312015509514686031193798241, 24431421930145927713526351934816506384811205836191828228900485331569907542066

Offset

0,3

Links

Table of n, a(n) for n=0..10.

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012.

Wikipedia, Young tableau

Formula

a(n) = A214722(n,n).

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])<j, 0, l[i+1][j]) and l[i][j]>
      `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], [n]]):
seq(a(n), n=0..8);

Mathematica

b[l_] := b[l] = With[{m = Length[l]}, If[Union[Flatten[l]] == {0}, 1, Sum[Sum[ If[l[[i, j]] > If[i == m || Length[l[[i+1]]]<j, 0, l[[i+1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j+1]]], b[ReplacePart[l, i -> ReplacePart[ l[[i]], j -> l[[i, j]]-1]]], 0], {j, Length[l[[i]]]}], {i, m}]]];
a[n_] := b[{Array[n&, n], {n}}];
Table[a[n], {n, 0, 8}] (* Jean-François Alcover, Aug 25 2021, after Alois P. Heinz *)

Crossrefs

Cf. A214722, A258586.

Sequence in context: A289904 A375104 A181028 * A337796 A159403 A221199

Adjacent sequences: A258580 A258581 A258582 * A258584 A258585 A258586

Keyword

nonn

Author

Alois P. Heinz, Nov 06 2015

Status

approved