Journal of Integer Sequences, Vol. 15 (2012), Article 12.6.3

Alternating Weighted Sums of Inverses of Binomial Coefficients


Renzo Sprugnoli
Dipartimento di Sistemi e Informatica
Viale Morgagni 65
50134 Firenze
Italy

Abstract:

We consider the alternating sums $ S^{(m)}_n = \sum_{k=0}^n (-1)^{n-k} k^m {n \choose k}^{-1}$, recently studied by Belbachir, Rahmani, and Sury, and obtain some results complementary to those found by the three authors, especially concerning generating functions, closed forms, and asymptotic approximation.

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(Concerned with sequences A008292 A034856.)

Received April 6 2012; revised version received June 13 2012. Published in Journal of Integer Sequences, June 19 2012.

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