  We find a generating function expressed as a continued fraction that
enumerates ordered trees by the number of vertices at different levels. Several
Catalan problems are mapped to an ordered-tree problem and their generating
functions also expressed as a continued fraction. Among these problems is the
enumeration of (132)-pattern avoiding permutations that have a given number of
increasing patterns of length k. This extends and illuminates a result of
Robertson, Wilf and Zeilberger for the case k=3.
