  Anisotropic flow measurements in heavy-ion collisions provide important
information on the properties of hot and dense matter. These measurements are
based on analysis of azimuthal correlations and might be biased by
contributions from correlations that are not related to the initial geometry,
so called non-flow. To improve anisotropic flow measurements advanced methods
based on multi-particle correlations (cumulants) have been developed to
suppress non-flow contribution. These multi-particle correlations can be
calculated by looping over all possible multiplets, however this quickly
becomes prohibitively CPU intensive. Therefore, the most used technique for
cumulant calculations is based on generating functions. This method involves
approximations, and has its own biases, which complicates the interpretation of
the results. In this paper we present a new exact method for direct
calculations of multi-particle cumulants using moments of the flow vectors.
