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Zbl 1210.11034
Liu, Hong-Mei; Qi, Shu-Hua; Ding, Shu-Yan
Some recurrence relations for Cauchy numbers of the first kind. (English)
[J] J. Integer Seq. 13, No. 3, Article ID 10.3.8, 7 p., electronic only (2010). ISSN 1530-7638/e

The authors present some recurrence relations for the Cauchy numbers of the first kind $(b_n)_{n\geq 0}$, using the Stirling numbers of the first kind $(s(n,k))_{n,k\geq 0}$. For example: $$\sum_{j=0}^n\binom{n+k}{j}s(n-j+k,k)b_j=\frac{n+k}{k}s(n+k-1,k-1),\quad n\geq 0, k\geq 1. $$
[Florin Nicolae (Berlin)]

MSC 2000:: *11B83 Special sequences of integers and polynomials
05A19 Combinatorial identities
11B73 Bell and Stirling numbers

Keywords: Cauchy numbers; Stirling numbers; combinatorial identities

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