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 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