  In this paper, we show that the r-Stirling numbers of both kinds, the
r-Whitney numbers of both kinds, the r-Lah numbers and the r-Whitney-Lah
numbers form particular cases of family of polynomials forming a generalization
of the partial Bell polynomials. We deduce the generating functions of several
restrictions of these numbers. In addition, a new combinatorial interpretations
is presented for the r-Whitney numbers and the r-Whitney-Lah numbers.
