The energy levels of two and three anyons in a two-dimensional parabolic quantum dot and a perpendicular magnetic field are computed as power series in $1/|J|,$ where $J$ is the angular momentum. The particles interact repulsively through a Coulombic $(1/r)$ potential. In the two-anyon problem, the reached accuracy is better than one part in ${10}^{5}.$ For three anyons, we study the combined effects of anyon statistics and Coulomb repulsion in the ``linear'' anyonic states.
