  Groupoids graded by the groupoid of bijections between finite sets admit
generating functions which encode the groupoid cardinalities of their graded
components. We use analytic continuation of such generating functions to define
a complex-valued cardinality for groupoids whose usual groupoid cardinality
diverges. The complex nature of such a cardinality invariant is shown to
reflect a recursion of structure which we refer to as `nested equivalence'.
