eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2333-1232
2019-04-24
7
2
56
58
10.12691/tjant-7-2-5
TJANT2019725
article
An Alternative Proof of a Closed Formula for Central Factorial Numbers of the Second Kind
Feng Qi
1
2
Guo-Sheng Wu
3
Bai-Ni Guo
bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com
4
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, 028043, Inner Mongolia, China
School of Computer Science, Sichuan Technology and Business University, Chengdu 611745, Sichuan, China
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454010, Henan, China
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.
http://pubs.sciepub.com/tjant/7/2/5/tjant-7-2-5.pdf
alternative proof
closed formula
central factorial number of the second kind
Bell polynomial of the second kind
finite sum
falling factorial
open problem