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P. L. Butzer, M. Schmidt, E. L. Stark, and L. Vogt, Central factorial numbers; their main properties and some applications, Numer. Funct. Anal. Optim. 10 (1989), no. 5-6, 419-488.

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Article

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

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


Turkish Journal of Analysis and Number Theory. 2019, Vol. 7 No. 2, 56-58
DOI: 10.12691/tjant-7-2-5
Copyright © 2019 Science and Education Publishing

Cite this paper:
Feng Qi, Guo-Sheng Wu, 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.

Correspondence to: Bai-Ni  Guo, School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China. Email: bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com

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.

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