Abstract
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 language | English (US) |
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Title of host publication | Integers |
Subtitle of host publication | Annual Volume 2013 |
Publisher | Walter de Gruyter GmbH |
Pages | 149-161 |
Number of pages | 13 |
ISBN (Electronic) | 9783110298161 |
ISBN (Print) | 9783110298116 |
DOIs | |
State | Published - Jan 1 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics