Some polynomials related to Dowling lattices and x-Stieltjes moment sequences

In this paper, we first introduce two sequences of polynomials, which unify many well-known polynomials related to Dowling lattices, including the Bell polynomials and the Dowling polynomials. Then we show the x-Stieltjes moment property of these polynomial sequences by their continued fractions and a criterion based on Sokal, Wang and Zhu independently.