  The associated Buchsbaum-Rim multiplicities of a module are a descending
sequence of non-negative integers. These invariants of a module are a
generalization of the classical Hilbert-Samuel multiplicity of an ideal. In
this article, we compute the associated Buchsbaum-Rim multiplicity of a direct
sum of cyclic modules and give a formula for the second to last positive
Buchsbaum-Rim multiplicity in terms of the ordinary Buchsbaum-Rim and
Hilbert-Samuel multiplicities. This is a natural generalization of a formula
given by Kirby and Rees.
