Generalized binomial expansions and bernoulli polynomials

Research output: Chapter in Book/Report/Conference proceedingChapter


We investigate generalized binomial expansions that arise from two-dimensional sequences satisfying a broad generalization of the triangular recurrence for binomial coefficients. In particular, we present a new combinatorial formula for such sequences in terms of a ‘shift by rank’ quasi-expansion based on ordered set partitions. As an application, we give a new proof of Dilcher’s formula for expressing generalized Bernoulli polynomials in terms of classical Bernoulli polynomials.

Original languageEnglish (US)
Title of host publicationIntegers
Subtitle of host publicationAnnual Volume 2013
PublisherWalter de Gruyter GmbH
Number of pages13
ISBN (Electronic)9783110298161
ISBN (Print)9783110298116
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics


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