Symmetric recurrence relations and binomial transforms

JOURNAL OF NUMBER THEORY

卷:133

Article

Mu, Yan-Ping

关键词: Recurrence relation;    Binomial transform;    Bernoulli numbers;   

DOI  :  10.1016/j.jnt.2013.03.003

来源: Elsevier

【 摘 要 】

We consider a family of sums which satisfy symmetric recurrence relations. A sufficient and necessary condition for the existence of such recurrence relations is given. Let us call a pair of sequence (a(n), b(n)) a binomial pair if a(n) is the binomial transform of b(n). We give some ways of constructing new binomial pairs from old ones. We further generalize the binomial transform by adding a parameter and show that the generalized binomial transform is an involution. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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