  A generalized version of Groeneveld's convergence criterion for the virial
expansion and generating functionals for weighted $2$-connected graphs is
proven. The criterion works for inhomogeneous systems and yields bounds for the
density expansions of the correlation functions $\rho_s$ (a.k.a. distribution
functions or factorial moment measures) of grand-canonical Gibbs measures with
pairwise interactions. The proof is based on recurrence relations for graph
weights related to the Kirkwood-Salsburg integral equation for correlation
functions. The proof does not use an inversion of the density-activity
expansion, however a Moebius inversion on the lattice of set partitions enters
the derivation of the recurrence relations.
