Journal of Integer Sequences, Vol. 15 (2012), Article 12.2.8

Alternating Sums of the Reciprocals of Binomial Coefficients


Hacène Belbachir and Mourad Rahmani
University of Sciences and Technology Houari Boumediene
Faculty of Mathematics
P. O. Box 32
El Alia, Bab-Ezzouar 16111
Algiers
Algeria

B. Sury
Statistics & Mathematics Unit
Indian Statistical Institute
8th Mile Mysore Road
Bangalore 560059
India

Abstract:

We investigate summations of the form $ \sum\nolimits_{0\leq k\leq n}\left( -1\right) ^{k}k^{m}\binom{n}{k}^{-1}$. We give closed formulae in terms of the Akiyama-Tanigawa matrix. Recurrence formulae, ordinary generating functions and some other results are also given.

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(Concerned with sequences A008275 A008277 A008292 A028246.)

Received July 27 2011; revised version received January 13 2012. Published in Journal of Integer Sequences, January 14 2012.

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