Observations on some particular power series

摘要

To place the content of this note into some sort of context, the simple results presented here emerged whilst I was carrying out some investigations into the enumeration of partitions associated with a particular type of multiset. A multiset extends the notion of a set to allow for repeated elements. For example, {1,2,2,2,3,4,5,5} is one in which the elements 2 and 5 havemultiplicities 3 and 2, respectively, with the remaining elements each possessing multiplicity 1. See [1] or [2] for the formal definition of a multiset.