Identities and congruences for a new sequence

2010/12/17 by Zhi-Hong Sun, Sun, Zhi-Hong
Mathematics · #11A07 #11B68 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A07 #msc:11B68

paper · pdf · doi:10.48550/arxiv.1012.4034

18 pages

arxiv created 2010/12/17 · openalex publication_date 2010/12/17 · arxiv updated 2010/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence \U_n\ given by U₀=1 and U_n=-2∑_k=1^[n/2]\binom n2kU_n-2k (n≥ 1), and establish many recursive formulas and congruences involving \U_n\.

Related

• On the further properties of \U_n\
• Congruences for sequences analogous to Euler numbers
• On the properties of even and odd sequences
• Congruences involving the reciprocals of central binomial coefficients
• A new kind of numbers and related congruences