[antiterra]

And, if you want to know more about generating functions, you can check out the book "generatingfunctionology" by the recently late Herbert Wilf gratis at http://www.math.upenn.edu/~wilf/DownldGF.html

[tmoertel]

Another great resource on generating functions is Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick:

http://algo.inria.fr/flajolet/Publications/book.pdf