A new approach for proving or generating combinatorial identities

Abstract

A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n+1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them a priori), simply by assigning adequate values to those parameters. The identities all flow swiftly from one simple theorem and the presentation is self-contained.