Authors’ abstract: “A formula in the first and the last author’s paper in Ars Comb. 17, 243-254 (1984; Zbl 0548.60013), for the number of lattice paths from the origin to a point (a,b) which do not cross the line \(y=kx\) is correct only in special cases. Those cases are noted and in other cases the equality is replaced by upper and lower bounds.”