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Displaying similar documents to “The Euler series transformation and the binomial identities of Ljunggren, Munarini and Simons.”

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

István Mező, Ayhan Dil (2009)

Open Mathematics

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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.

Some finite generalizations of Euler's pentagonal number theorem

Ji-Cai Liu (2017)

Czechoslovak Mathematical Journal

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Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.