2019/02/16 by René Gy, Gy, René
Mathematics · #05A15 (Primary) 11B68 (Primary) 11B73 (Primary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1902.09309
openalex publication_date 2019/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Congruences modulo prime powers involving generalized Harmonic numbers are known. While looking for similar congruences, we have encountered a curious triangular array of numbers indexed with positive integers n,k, involving the Bernoulli and cycle Stirling numbers. These numbers are all integers and they vanish when n-k is odd. This triangle has many similarities with the Stirling triangle. In particular, we show how it can be extended to negative indices and how this extension produces a \it second kind of such integers which may be considered as a new generalization of the Genocchi numbers and for which a generating function is easily obtained. But our knowledge of these integers remains limited, especially for those of the \it first kind.