Abstract
AbstractIn this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. The connections between the new numbers and the Stirling numbers are presented. In addition, we give the probability distribution of the unsigned r-central factorial numbers with even indices. Finally, we consider the r-central factorial matrices and study some of their properties.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference30 articles.
1. Acikgoz, M., Araci, S., Duran, U.: Some $(p; q)$-analogues of Apostol type numbers and polynomials. Acta Comment. Univ. Tartu Math. 23(1), 37–50 (2019)
2. Araci, S., Duran, U., Acikgoz, M.: On weighted q-Daehee polynomials with their applications. Indag. Math. 30, 365–374 (2019)
3. Bóna, M.: Combinatorics of Permutations. Chapman & Hall/CRC, London (2004)
4. Butzer, P.L., Schmidt, K., Stark, E.L., Vogt, L.: Central factorial numbers; their main properties and some applications. Numer. Funct. Anal. Optim. 10(5&6), 419–488 (1989)
5. Call, G.S., Velleman, D.J.: Pascal’s matrices. Am. Math. Mon. 100, 372–376 (1993)