  We compute the limiting distribution of height of a random discrete excursion
with step sets consisting of one positive step 1 and arbitrary finite set of
non-positive integers. The limit law is the supremum of a Brownian excursion.
This is well-known for Dyck and Motzkin paths. We apply a representation of the
length and height generating function in terms of certain Schur polynomials put
forward in a 2008 paper by Bousquet-Melout which leads to a form of the moment
generating functions amenable to a Mellin transform analysis.
