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

Open Mathematics (2009)

- Volume: 7, Issue: 2, page 310-321
- ISSN: 2391-5455

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topIstván Mező, and Ayhan Dil. "Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence." Open Mathematics 7.2 (2009): 310-321. <http://eudml.org/doc/269683>.

@article{IstvánMező2009,

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.},

author = {István Mező, Ayhan Dil},

journal = {Open Mathematics},

keywords = {Harmonic numbers; Hyperharmonic numbers; r-Stirling numbers; Fibonacci numbers; Euler-Seidel matrices; Euler-Seidel matrix; hyperharmonic numbers; -Stirling numbers; hypergeometric functions},

language = {eng},

number = {2},

pages = {310-321},

title = {Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence},

url = {http://eudml.org/doc/269683},

volume = {7},

year = {2009},

}

TY - JOUR

AU - István Mező

AU - Ayhan Dil

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

JO - Open Mathematics

PY - 2009

VL - 7

IS - 2

SP - 310

EP - 321

AB - 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.

LA - eng

KW - Harmonic numbers; Hyperharmonic numbers; r-Stirling numbers; Fibonacci numbers; Euler-Seidel matrices; Euler-Seidel matrix; hyperharmonic numbers; -Stirling numbers; hypergeometric functions

UR - http://eudml.org/doc/269683

ER -

## References

top- [1] Benjamin A.T., Gaebler D.J., Gaebler R.P., A combinatorial approach to hyperharmonic numbers, Integers, 2003, 3, 1–9 Zbl1128.11309
- [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 Zbl0866.00001
- [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 Zbl0925.05025
- [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 Zbl0836.00001
- [9] Koshy T., Fibonacci and Lucas numbers with applications, Wiley-Interscience, New York, 2001 Zbl0984.11010
- [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] Zbl1174.11026
- [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

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