Generating functions of lattice paths

We recall the main types of lattice paths, which are sequences in the lattice of integer coordinates points in the plane. We start with the fundamental central lattice paths and Dyck paths and proceed in elementary terms through recently introduced lattice paths. For every type, we consider the respective generating function. In fact, through our approach (via Riordan arrays), various entries of the On-Line Encyclopedia of Integer Sequences are unified, clarified, and simplified.