Book on combinatorial identities Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem in two different ways)?

This may not be what you are looking for, but you Gian-Carlo Rota and Kenneth Baclawski's Introduction to Probability and Random Processes is freely available for download online and is a classic introduction to probability, with an emphasis on the underlying combinatorics.  You could certainly get a lot of ideas for how to generate the types of identities you are looking for, but as far as I know it does not have an encyclopedic list of such identities.
