  Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two
properties of $T_n$ are proved: (1) The {\em last descent} and {\em last index
minus one} statistics are equidistributed over $T_n$, and also over subsets of
permutations whose inverse has an (almost) prescribed descent set. An analogous
result holds for Dyck paths. (2) The sign-and-last-descent enumerators for
$T_{2n}$ and $T_{2n+1}$ are essentially equal to the last-descent enumerator
for $T_n$. The proofs use a recursion formula for an appropriate multivariate
generating function.
