cp's OEIS Frontend

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

%I A258583 #20 Aug 25 2021 14:54:27
%S A258583 1,1,16,5471,75965484,70692556053053,6614511157454872712100,
%T A258583 87353366195666890516586545068535,
%U A258583 217757982462900115559339884671224174403391534,132100470099008733697710444705793312015509514686031193798241,24431421930145927713526351934816506384811205836191828228900485331569907542066
%N A258583 Number of solid standard Young tableaux of shape [[{n}^n],[n]].
%H A258583 S. B. Ekhad, D. Zeilberger, <a href="https://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229v1 [math.CO], 2012.
%H A258583 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A258583 a(n) = A214722(n,n).
%p A258583 b:= proc(l) option remember; local m; m:= nops(l);
%p A258583       `if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>
%p A258583       `if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>
%p A258583       `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
%p A258583        j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
%p A258583     end:
%p A258583 a:= n-> b([[n$n], [n]]):
%p A258583 seq(a(n), n=0..8);
%t A258583 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}]]];
%t A258583 a[n_] := b[{Array[n&, n], {n}}];
%t A258583 Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Aug 25 2021, after _Alois P. Heinz_ *)
%Y A258583 Cf. A214722, A258586.
%K A258583 nonn
%O A258583 0,3
%A A258583 _Alois P. Heinz_, Nov 06 2015