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In this paper (as in previous ones) we identify and investigate polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_n^{(v)}\,(x)$$\end{document} featuring at least one additional parameter ν besides their argument x and the integer n identifying their degree. They are orthogonal (provided the parameters they generally feature fit into appropriate ranges) inasmuch as they are defined via standard three-term linear recursion relations; and they are interesting inasmuch as they obey a second linear recursion relation involving shifts of the parameter ν and of their degree n, and as a consequence, for special values of the parameter ν, also remarkable factorizations, often having a …