New combinatorial proof of the multiple binomial coefficient identity

Abstract

Introduction/purpose: In this paper a new combinatorial proof of an already existing multiple sum with multiple binomial coefficients is given. The derived identity is related to the Fibonacci numbers. Methods: Combinatorial reasoning is used to obtain the results. Results: The already known identity was obtained by using a new combinatorial reasoning. Conclusions: The new combinatorial reasoning led to the solution of the already existing identity.

Keywords

• fibonacci numbers
• combinatorics