The Hankel transform of \(q\)-noncentral Bell numbers (Q1751368)

Summary: We define two forms of \(q\)-analogue of noncentral Stirling numbers of the second kind and obtain some properties parallel to those of noncentral Stirling numbers. Certain combinatorial interpretation is given for the second form of the \(q\)-analogue in the context of 0-1 tableaux which, consequently, yields certain additive identity and some convolution-type formulas. Finally, a \(q\)-analogue of noncentral Bell numbers is defined and its Hankel transform is established.