  We consider a random permutation drawn from the set of 132-avoiding
permutations of length $n$ and show that the number of occurrences of another
pattern $\sigma$ has a limit distribution, after scaling by
$n^{\lambda(\sigma)/2}$ where $\lambda(\sigma)$ is the length of $\sigma$ plus
the number of descents. The limit is not normal, and can be expressed as a
functional of a Brownian excursion. Moments can be found by recursion.
