English

Convoluted convolved Fibonacci numbers

Combinatorics 2007-05-23 v1

Abstract

The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the numerical evaluation of a certain number theoretical constant. This note is a case study of the transform {1/n}\sum_{d|n}mu(d)f(z^d)^{n/d}, with f any formal series and mu the Moebius function), which is studied in a companion paper entitled `The formal series Witt transform'.

Keywords

Cite

@article{arxiv.math/0311205,
  title  = {Convoluted convolved Fibonacci numbers},
  author = {Pieter Moree},
  journal= {arXiv preprint arXiv:math/0311205},
  year   = {2007}
}

Comments

12 pages, 3 tables