  For a system of bosons that interact through a class of general memory
kernels, a recurrence relation for the partition function is derived within the
path-integral formalism. This approach provides a generalization to previously
known treatments in the literature of harmonically coupled systems of identical
particles. As an example the result is applied to the specific heat of a
simplified model of an open quantum system of bosons, harmonically coupled to a
reservoir of distinguishable fictitious masses.
