The book Proofs that Really Count: The Art of Combinatorial Proof, by Art Benjamin and Jenny Quinn, contains a large number of combinatorial identities with no known combinatorial proof. (See the end of most of the chapters.) As the subtitle indicates, it is also a great reference for those interested in combinatorial proof techniques.

The book Proofs that Really Count: The Art of Combinatorial Proof, by Art Benjamin and Jenny Quinn, contains a large number of combinatorial identities with no known combinatorial proof. (See the end of most of the chapters.) As the subtitle indicates, it is also a great reference for those interested in combinatorial proof techniques.