New Proof of the Property of Stirling Number Based on Fubini Polynomials

Abstract

The main purpose of this article is using the elementary methods and the properties of the Fubini polynomials to study the congruence properties of a signless Stirling number of the first kind and solve a conjecture proposed by J. H. Zhao and Z. Y. Chen. Without a doubt, the novel approach employed in this work provides a useful reference for researching the congruence properties of other nonlinear binary recursive sequences.