  We consider various classes of Motzkin trees as well as lambda-terms for
which we derive asymptotic enumeration results. These classes are defined
through various restrictions concerning the unary nodes or abstractions,
respectively: We either bound their number or the allowed levels of nesting.
The enumeration is done by means of a generating function approach and
singularity analysis. The generating functions are composed of nested square
roots and exhibit unexpected phenomena in some of the cases. Furthermore, we
present some observations obtained from generating such terms randomly and
explain why usually powerful tools for random generation, such as Boltzmann
samplers, face serious difficulties in generating lambda-terms.
