A258586 - OEIS

%I #13 Jul 19 2017 20:08:03

%S 1,2,936,1825221320,70351928759681296000,

%T 160978956785364112335731878007698260,

%U 51488321677815455036453939239317069333712945710369620220,4648889159675386017282064494039528050991187044317172798976485350954735075040045120

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

%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%p b:= proc(l) option remember; local m; m:= nops(l);

%p       `if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>

%p       `if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>

%p       `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(

%p        j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))

%p     end:

%p a:= n-> b([[n$(n+1)], [n]$n]):

%p seq(a(n), n=0..5);

%Y Cf. A214722, A258583.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Nov 06 2015