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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
mailto:hacenebelbachir@gmail.comhacenebelbachir@gmail.com
mailto:mrahmani@usthb.dzmrahmani@usthb.dz

B. Sury
Statistics & Mathematics Unit
Indian Statistical Institute
8th Mile Mysore Road
Bangalore 560059
India
mailto:sury@isibang.ac.insury@isibang.ac.in

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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.