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arXiv · 2604.23223

Une curieuse égalité entre deux sommes de produits de coefficients binomiaux

Flavien Mabilat
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Abstract

We will show in this text that, for all non-negative integers $n$ and $l$, the following equality is verified: \[\sum_{i=0}^{l} {n-i \choose i}{l+i \choose 2i+1}=\sum_{i=0}^{l} {n-i \choose i-1}{l+i \choose 2i}.\] We will first address the case where $l \leq n$, for which both sums contain only classical binomial coefficients. Then, we will consider the general framework using generalized binomial coefficients.

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Flavien Mabilat. 2026-04-25. Une curieuse égalité entre deux sommes de produits de coefficients binomiaux. https://arxiv.org/abs/2604.23223

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