On the properties of even and odd sequences

2014/02/20 by Sun, Zhi-Hong
#05A15 #05A19 #11A07 #11B39 #11B68 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1402.5091

Abstract

In this paper we continue to investigate the properties of those sequences \a_n\ satisfying the condition ∑_k=0ⁿ\binom nk(-1)^ka_k=± a_n (n≥ 0). As applications we deduce new recurrence relations and congruences for Bernoulli and Euler numbers.

Related

• Identities and congruences for a new sequence
• Congruences for sequences analogous to Euler numbers
• A new kind of numbers and related congruences
• Recurrence formulas with gaps for Bernoulli and Euler polynomials
• Congruences involving binomial coefficients and Lucas sequences