  We show that the bound states in a three-body system display a Coulomb series
with a Gaussian cut-off provided: (i) the system consists of a light particle
and two heavy bosonic ones, (ii) the heavy-light short-range potential has a
resonance in the $p$-wave scattering amplitude, and (iii) all three particles
move in two space dimensions. For a decreasing mass ratio this quasi-Coulomb
series merges into a pure Coulombic one.
