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.

**Answer**

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.

**Attribution***Source : Link , Question Author : Community , Answer Author : darij grinberg*