The virial expansion of the collective mobility (sedimentation) coefficient is considered for hard sphere suspensions at equilibrium. The term of the second order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy. To achieve that we represent the collective mobility coefficient as the sum of convergent integrals over particle configurations. In this way the short-wave-number limit k-->0 is avoided. Moreover, an efficient numerical procedure is applied to evaluate the hydrodynamic interactions. The algorithm is based on the multipole expansion, corrected for lubrication. The method allows us to analyze contributions to the collective mobility coefficient from different configurations of three particles and to select the dominant part. This suggests a general approximation scheme.