Enumerating a class of lattice paths

AbstractLet D0(n) denote the set of lattice paths in the xy-plane that begin at (0,0), terminate at (n,n), never rise above the line y=x and have step set S={(k,0):k∈N+}∪{(0,k):k∈N+}. Let E0(n) denote the set of lattice paths with step set S that begin at (0,0) and terminate at (n,n). Using primarily the symbolic method (R. Sedgewick, P. Flajolet, An Introduction to the Analysis of Algorithms, Addison-Wesley, Reading, MA, 1996) and the Lagrange inversion formula we study some enumerative problems associated with D0(n) and E0(n)