Combinatorial properties of the numbers of tableaux of bounded height
  We introduce an infinite family of lower triangular matrices $\Gamma^{(s)}$, where $\gamma_{n,i}^s$ counts the standard Young tableaux on $n$ cells and with at most $s$ columns on a suitable subset of shapes. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number $\tau_s(n)$ of tableaux on $n$ cells and with at most $s$ columns. 
M.Barnabei, F.Bonetti, and M.Silimbani