Divisibility properties of the r-Bell numbers and polynomials

In the present article we extend several arithmetical results to a family of generalized Bell numbers called r-Bell numbers. In particular, we generalize some congruences such as Touchard's congruence, Sun-Zagier congruence for Bell and derangement numbers and polynomials, among others. We also describe the behavior of the 2-adic valuation of the r-Bell numbers.