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

István Mező 1  and Ayhan Dil 2
  • 1 Department of Algebra and Number Theory, Institute of Mathematics, University of Debrecen, Debrecen, Hungary
  • 2 Department of Mathematics, Faculty of Art and Science, University of Akdeniz, Antalya, Turkey

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.

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