Closed-form expression for Hankel determinants of the Narayana polynomials
- 151 Downloads
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.
KeywordsNarayana numbers Hankel transform orthogonal polynomials
MSC 201011Y55 34A25
Unable to display preview. Download preview PDF.
- P. Barry: On integer-sequences-based constructions of generalized Pascal triangles. J. Integer Seq. 59 (2006). Article 06.2.4. Electronic only.Google Scholar
- P. Barry, A. Hennessy: Notes on a family of Riordan arrays and associated integer Hankel transforms. J. Integer Seq. 12 (2009). Article ID 09.5.3. Electronic only.Google Scholar
- M. Chamberland, C. French: Generalized Catalan numbers and generalized Hankel transformations. J. Integer Seq. 10 (2007).Google Scholar
- A. Cvetković, P. M. Rajković, M. Ivković: Catalan Numbers, the Hankel transform, and Fibonacci numbers. J. Integer Seq. 5 (2002).Google Scholar
- O. Eğecioğlu, T. Redmond, C. Ryavec: Almost product evaluation of Hankel determinants. Electron. J. Comb. 15,#R6 (2008).Google Scholar
- M. Garcia Armas, B.A. Sethuraman: A note on the Hankel transform of the central binomial coefficients. J. Integer Seq. 11 (2008). Article ID 08.5.8.Google Scholar
- W. Gautschi: Orthogonal polynomials: Applications and computation. In: Acta Numerica Vol. 5 (A. Iserles, ed.). Cambridge University Press, Cambridge, 1996, pp. 45–119.Google Scholar
- J. W. Layman: The Hankel transform and some of its properties. J. Integer Seq. 4 (2001). Article 01.1.5. Electronic only.Google Scholar
- P. A. MacMahon: Combinatorial Analysis, Vols. 1 and 2. Cambridge University Press, Cambridge, 1915, 1916, reprinted by Chelsea, 1960.Google Scholar
- N. J. A. Sloane: The On-Line Encyclopedia of Integer Sequences; available at http://www.research.att.com/~njas/sequences.
- R. A. Sulanke: Counting lattice paths by Narayana polynomials. Electron. J. Comb. 7 (2000). #R40.Google Scholar