An Alternative Proof of a Closed Formula for Central Factorial Numbers of the Second Kind

Feng Qi^{1, 2}, Guo-Sheng Wu³ and Bai-Ni Guo^4,

¹College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, 028043, Inner Mongolia, China

²School of Mathematical Sciences, Tianjin Polytechnic, University, Tianjin 300387, China

³School of Computer Science, Sichuan Technology and Business University, Chengdu 611745, Sichuan, China

⁴School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China

Cite this paper:
Feng Qi, Guo-Sheng Wu and Bai-Ni Guo. An Alternative Proof of a Closed Formula for Central Factorial Numbers of the Second Kind. Turkish Journal of Analysis and Number Theory. 2019; 7(2):56-58. doi: 10.12691/tjant-7-2-5

Abstract

In the short note, by virtue of several formulas and identities for special values of the Bell polynomials of the second kind, the authors provide an alternative proof of a closed formula for central factorial numbers of the second kind. Moreover, the authors pose two open problems on closed form of a special Bell polynomials of the second kind and on closed form of a finite sum involving falling factorials.

Keywords:
alternative proof closed formula central factorial number of the second kind Bell polynomial of the second kind finite sum falling factorial open problem

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