Books/Resources on generating functions
Solution 1:
The second edition of Herbert Wilf’s generatingfunctionology is freely available here in PDF form. Concrete Mathematics, by Graham, Knuth, and Patashnik, has a very nice introduction in Chapter $7$ and is a very fine book all around.
Solution 2:
Look into generatingfunctionology by Herbert S. Wilf.
It's precisely about generating functions! Fairly short but thorough. From the link (Wilf's website), you can
- download the $2$nd edition of the text (as a pdf document),
- download a version of the book with hyperlinks to be read on-line,
- or else click on the link to the publisher if you'd like to purchase the $3$rd edition.
- (Perhaps you can obtain a hard copy from you library.)
From MIT (and a course taught there), you can download a pdf dedicated to generating functions, which is outlined nicely, and allows you to access the topics in order, or those of interest.
Finally, see Ch. 10: Generating Functions of the freely available text authored by Grinstead and Laurie Snell, and published by the AMS: Introduction to Probability.
You might want to invest in Concrete Mathematics by Graham, Knuth, and Patashnik. It has a nicely written introduction to generating functions,
Solution 3:
Another great freely (and legally!) available online resource is Flajolet and Sedgewick's Analytic Combinatorics, which in addition to having lots of material about generating functions also has lots of material about asymptotic analysis.