A Dyck path of length $2n$ is a diagonal lattice path from $(0,0)$ to $(2n,0)$, with $n$ up-steps (along the vector $(1,1)$) and $n$ down-steps (along the vector $(1,−1)$), such that the path never goes below the $x$-axis. The number of Dyck paths of length $2n$ is $\tfrac{1}{n+1}\binom{2n}{n}$, i.e. the $n$th Catalan number.
Motzkin paths are slightly more general than Dyck paths: such paths permit level steps (along the vector $(0,1)$). Consider the restricted class of Motzkin paths that only permit level steps at the $x$-axis (or ground-level). How many Motzkin paths of length $n$ are in this restricted class?