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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 24, 2009

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

  • István Mező EMAIL logo and Ayhan Dil
From the journal Open Mathematics

Abstract

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.

MSC: 11B83

[1] Benjamin A.T., Gaebler D.J., Gaebler R.P., A combinatorial approach to hyperharmonic numbers, Integers, 2003, 3, 1–9 Search in Google Scholar

[2] Broder A.Z., The r-Stirling numbers, Discrete Math., 1984, 49, 241–259 http://dx.doi.org/10.1016/0012-365X(84)90161-410.1016/0012-365X(84)90161-4Search in Google Scholar

[3] Conway J.H., Guy R.K., The book of numbers, Copernicus, New York, 1996 10.1007/978-1-4612-4072-3Search in Google Scholar

[4] Dil A., Mean values of Dedekind sums, M.Sc. in Mathematics, University of Akdeniz, Antalya, December 2005 (in Turkish) Search in Google Scholar

[5] Dil A., Kurt V, Cenkci M., Algorithms for Bernoulli and allied polynomials, J. Integer Seq., 2007, 10, Article 07.5.4. Search in Google Scholar

[6] Dumont D., Matrices d’Euler-Seidel, Séminaire Lotharingien de Combinatoire, 1981 Search in Google Scholar

[7] Euler L., De transformatione serierum, Opera Omnia, series prima, Vol. X, Teubner, 1913 Search in Google Scholar

[8] Graham R.L., Knuth D.E., Patashnik O., Concrete mathematics, Addison-Wesley Publishing Company, Reading, MA, 1994 Search in Google Scholar

[9] Koshy T., Fibonacci and Lucas numbers with applications, Wiley-Interscience, New York, 2001 10.1002/9781118033067Search in Google Scholar

[10] Mező I., New properties of r-Stirling series, Acta Math. Hungar., 2008, 119, 341–358 http://dx.doi.org/10.1007/s10474-007-7047-910.1007/s10474-007-7047-9Search in Google Scholar

[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 Search in Google Scholar

Published Online: 2009-5-24
Published in Print: 2009-6-1

© 2009 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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