Herbert S. Wilf 
generatingfunctionology [PDF ebook] 
Third Edition

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in – Combinatorics – Probability Theory – Statistics – Theory of Markov Chains – Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.