Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

• Autorzy: István Mező , Ayhan Dil
• Języki publikacji: EN

Abstrakty

EN

In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.

Słowa kluczowe

EN

Harmonic numbers; Hyperharmonic numbers; r-Stirling numbers; Fibonacci numbers; Euler-Seidel matrices

Kategorie tematyczne

• 11B83: Special sequences and polynomials

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 310-321

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

István Mező

• Department of Algebra and Number Theory, Institute of Mathematics, University of Debrecen, Debrecen, Hungary

autor

Ayhan Dil

• Department of Mathematics, Faculty of Art and Science, University of Akdeniz, Antalya, Turkey

Bibliografia

• [1] Benjamin A.T., Gaebler D.J., Gaebler R.P., A combinatorial approach to hyperharmonic numbers, Integers, 2003, 3, 1–9
• [2] Broder A.Z., The r-Stirling numbers, Discrete Math., 1984, 49, 241–259 http://dx.doi.org/10.1016/0012-365X(84)90161-4[Crossref]
• [3] Conway J.H., Guy R.K., The book of numbers, Copernicus, New York, 1996
• [4] Dil A., Mean values of Dedekind sums, M.Sc. in Mathematics, University of Akdeniz, Antalya, December 2005 (in Turkish)
• [5] Dil A., Kurt V, Cenkci M., Algorithms for Bernoulli and allied polynomials, J. Integer Seq., 2007, 10, Article 07.5.4.
• [6] Dumont D., Matrices d’Euler-Seidel, Séminaire Lotharingien de Combinatoire, 1981
• [7] Euler L., De transformatione serierum, Opera Omnia, series prima, Vol. X, Teubner, 1913
• [8] Graham R.L., Knuth D.E., Patashnik O., Concrete mathematics, Addison-Wesley Publishing Company, Reading, MA, 1994
• [9] Koshy T., Fibonacci and Lucas numbers with applications, Wiley-Interscience, New York, 2001
• [10] Mező I., New properties of r-Stirling series, Acta Math. Hungar., 2008, 119, 341–358 http://dx.doi.org/10.1007/s10474-007-7047-9[WoS][Crossref]
• [11] Seidel L., Über eine einfache Enstehung weise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsberichte der Münch. Akad. Math. Phys. Classe, 1877, 157–187

Identyfikatory

DOI

10.2478/s11533-009-0008-5