  We examine an identity originally stated in Ramanujan's ``lost notebook'' and
first proven algebraically by Andrews and combinatorially by Kim. We give two
independent combinatorial proofs and interpretations of this identity, which
also extends an identity recently proven by Pak and Waarnar related to the
product of partial theta functions: First, we give a direct combinatorial
proof, using the involution principle, of a special case of the identity, and
extend this into a direct combinatorial proof of the full identity as written.
Second, we show that the identity can be rewritten, using minor algebraic
manipulation, into an identity that can be proven with a direct bijection. We
provide such a bijection using a generalization of a standard bijection from
partition theory.
