Explicit formulas using partitions of integers for numbers defined by recursion
Number Theory
2018-02-02 v2 Combinatorics
Abstract
In this article we obtain an explicit formula in terms of the partitions of the positive integer to express the -th term of a wide class of sequences of numbers defined by recursion. Our proof is based only on arithmetics. We compare our result with similar formulas obtained with different approaches already in the XIX century. Examples are given for Bernoulli, Euler and Fibonacci numbers.
Keywords
Cite
@article{arxiv.1211.1440,
title = {Explicit formulas using partitions of integers for numbers defined by recursion},
author = {Giuseppe Fera and Vittorino Talamini},
journal= {arXiv preprint arXiv:1211.1440},
year = {2018}
}
Comments
13 pages pdf. v1 strong revised. Less examples. Added a section reporting other known proofs. Simplified the proof of the main theorem and the other theorems are now cutted or set in the examples section. Some references added and some cutted