Generating functions
Generating functions are often used in combinatorics as a formal way of expressing certain integer-valued sequences. For a comprehensive discussion of the topic, see Wilf's book, "generatingfunctionology." The second edition of this book is available for free online as a PDF download from this link.
Mathematical maturity edit
The reader probably wants a strong mathematical background in calculus, and should have an understanding of abstract algebra and some analysis (for when convergence issues do arise).