Poly-central factorial sequences and poly-central-Bell polynomials

Abstract

Abstract In this paper, we introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of the second kind respectively when k = 1 $k = 1$ . We also show some relations: between poly-central factorial sequences and power of x; between poly-central Bell polynomials and power of x; between poly-central Bell polynomials and the poly-Bell polynomials; between poly-central Bell polynomials and higher order type 2 Bernoulli polynomials of second kind; recurrence formula of poly-central Bell polynomials.

Keywords

• Central factorials
• Central-Bell polynomials and numbers
• Modified polyexponential functions
• Stirling numbers of the first and second kind
• Type 2 Bernoulli polynomials of the second kind