Hankel determinants of some polynomials arising in combinatorial analysis

In this paper we investigate Hankel determinants of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left| {c_{i + j} (t)} \right|_{ij = 0,...,n} $$ \end{document}, where cn(t) is one of a number of polynomials of combinatorial interest. We show how some results due to Radoux may be generalized, and also show how “stepped up” Hankel determinants of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left| {c_{i + j + k} (t)} \right|_{ij = 0,...,n} ,\;\;k = 1,2,...,$$ \end{document} may be evaluated.