A Strehl Version of Fourth Franel Sequence

TL;DR

This paper presents a combinatorial identity involving the fourth power of binomial coefficients related to Franel numbers, along with a combinatorial proof using double counting, expanding understanding of these sequences.

Contribution

It introduces a new combinatorial identity for Franel numbers and offers a novel proof based on double counting, enhancing combinatorial methods in this area.

Findings

Derived a new combinatorial identity involving Franel numbers

Provided a combinatorial proof using double counting techniques

Expanded understanding of the structure of Franel sequences

Abstract

We give a combinatorial identity related to the Franel numbers involving the sum of fourth power of binomial coefficients. Furthermore, investigating in J. Mikic's proof of the first Strehl Identity, we provide a combinatorial proof of this identity using the double counting argument.