A comprehensive list of binomial identities?

Is there a comprehensive resource listing binomial identities? I am more interested in combinatorial proofs of such identities, but even a list without proofs will do.


The most comprehensive list I know of is H.W. Gould’s Combinatorial Identities. It is available directly from him if you contact him. He also has some pdf documents available for download from his web site. Although he says they do “NOT replace [Combinatorial Identities] which remains in print with supplements,” they still contain many more binomial identities even than in Concrete Mathematics. In general, Gould’s work is a great resource for this sort of thing; he has spent much of his career collecting and proving combinatorial identities.

Added: Another useful reference is John Riordan’s Combinatorial Identities. It’s hard to pick one of its 250 pages at random and not find at least one binomial coefficient identity there. Unfortunately, the identities are not always organized in a way that makes it easy to find what you are looking for. Still it’s a good resource.

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