  We consider a class of lattice paths with certain restrictions on their
ascents and down steps and use them as building blocks to construct various
families of Dyck paths. We let every building block $P_j$ take on $c_j$ colors
and count all of the resulting colored Dyck paths of a given semilength. Our
approach is to prove a recurrence relation of convolution type, which yields a
representation in terms of partial Bell polynomials that simplifies the
handling of different colorings. This allows us to recover multiple known
formulas for Dyck paths and related lattice paths in an unified manner.
