The -Bell numbers.
Several generating functions for second-order recurrence sequences.
A generalization of Stirling numbers of the second kind via a special multiset.
Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions
There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.
Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence
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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