Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials

Bell polynomials and Fibonacci numbers

On degenerate numbers and polynomials related to the Stirling numbers and the Bell polynomials

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

Incomplete generalized Tribonacci polynomials and numbers

The main object of this paper is to present a systematic investigation of a new class of polynomials – incomplete generalized Tribonacci polynomials and a class of numbers associated with the familiar Tribonacci polynomials. The various results obtained here for these classes of polynomials and numbers include explicit representations, generating functions, recurrence relations and summation fo...

A Linear Binomial Recurrence and the Bell Numbers and Polynomials

By iterating (0.2), f(n + r) can be written as a linear combination of binomial coefficients with polynomial coefficients Arj(n), 0 ≤ j ≤ r − 1. The polynomials Arj(n) have various interesting properties. This paper provides a sampling of these properties, including two new ways to represent B(n) in terms of Arj (n).

Generalizations of the Bell Numbers and Polynomials and Their Properties

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers o...