  We count the number of vertices in plane trees and $k$-ary trees with given
outdegree, and prove that the total number of vertices of outdegree $i$ over
all plane trees with $n$ edges is ${2n-i-1 \choose n-1}$, and the total number
of vertices of outdegree $i$ over all $k$-ary trees with $n$ edges is
${k\choose i}{kn\choose n-i}$. For both results we give bijective proofs as
well as generating function proofs.
