  We consider both the Bolthausen-Sznitman and the Kingman coalescent
restricted to the partitions of $\{1, \ldots, n\}.$ Spectral decompositions of
the corresponding generators are derived. As an application we obtain a formula
for the Green's functions and a short derivation of the well-known formula for
the transition probabilities of the Bolthausen-Sznitman coalescent.
