  In this article, we compute the Buchsbaum-Rim function of two variables
associated to a direct sum of cyclic modules and give a formula for the last
positive associated Buchsbaum-Rim multiplicity in terms of the ordinary
Hilbert-Samuel multiplicity of an ideal. This is a generalization of a formula
for the last positive Buchsbaum-Rim multiplicity given by Kirby and Rees.
