The first-named author and S. K. Bhargava [Bull. Inst. Math., Acad. Sinica 7, 145–149 (1979; Zbl 0406.33008); Math. J. Ranchi Univ. 10, 74–80 (1979; Zbl 0485.33002)] considered an interesting special case of a certain class of polynomials \(\{g_ n^ c(x,t,s)\}_{n=0}^ \infty\) studied by the reviewer [Glasgow Math. J. 18, 105–108 (1977; Zbl 0329.33006); Boll. Unione Mat. Ital., V. Ser. A 17, 183–186 (1980; Zbl 0434.33012)]. The authors of this paper introduce and study a multivariable extension of the aforementioned special case. Among other results for these multivariable polynomials, they give explicit representations in terms of the (Srivastava-Daoust) generalized Lauricella function of several variables.