Falcão, Maria Irene; Malonek, Helmuth R. A note on a one-parameter family of non-symmetric number triangles. (English) Zbl 1268.30041 Opusc. Math. 32, No. 4, 661-673 (2012). The authors consider the following infinite array of numbers \[ T_s^k(n) = \frac{k!}{n_{(k)}}\frac{\left(\frac{n+1}{2}\right)_{(k-s)}}{(k-s)!}\frac{\left(\frac{n-1}{2}\right)_{(s)}}{s!}, \quad n,s \in \mathbb{N}, \; s=0,1, \dots, k \] where \(a_{(r)}\) denotes the Pochhammer symbol. These number were introduced to construct generalized Appell polynomials in the framework of Clifford analysis.In this paper the relation of these numbers with the elements of the Pascal triangle and the coefficients of the geometric series is discussed. Several arithmetical properties of the family of number triangles composed by fractions \(T_s^k(n)\) for different parameter values \(n\) in lines of height \(k\) and ordered from \(s =0\) up to \(s=k\) are proven. Reviewer: Regina de Almeida (Vila Real) Cited in 3 Documents MSC: 30G35 Functions of hypercomplex variables and generalized variables 05A19 Combinatorial identities, bijective combinatorics 11B65 Binomial coefficients; factorials; \(q\)-identities Keywords:number triangle; central binomial coefficient; binomial identity; generalized Appell polynomials; Clifford analysis Software:Quaternions PDF BibTeX XML Cite \textit{M. I. Falcão} and \textit{H. R. Malonek}, Opusc. Math. 32, No. 4, 661--673 (2012; Zbl 1268.30041) Full Text: DOI