  We establish a combinatorial connection between the sequence $(i_{n,k})$
counting the involutions on $n$ letters with $k$ descents and the sequence
$(a_{n,k})$ enumerating the semistandard Young tableaux on $n$ cells with $k$
symbols. This allows us to show that the sequences $(i_{n,k})$ are not
log-concave for some values of $n$, hence answering a conjecture due to F.
Brenti.
