In this paper the problem of exact summation over vibrational states of intermediate electronic level excited by resonance Raman scattering in a molecular system with an arbitrary number of vibrational modes is solved with the help of the coherent state representation. For matrix elements of the resonance Raman (RR) amplitude the expressions in the form of an integral and multiple series as well as recurrence relations are obtained. The interpretation of RR spectra of linear-chain mixed-valence platinum complexes is given as an illustration.