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.
• Epsilon Sandwiches https://www2.math.upenn.edu/~wilf/website/MAASpeech
In fact everything by Wilf that I've read is lovely: the paper "Recounting the rationals" (https://www2.math.upenn.edu/~wilf/website/recounting.pdf with Neil Calkin), and the book generatingfunctionology https://www2.math.upenn.edu/~wilf/DownldGF.html
Also go read Generatingfunctionology and Concrete Mathematics
Well-written and incredibly rewarding.