English

Asymptotics of the Euler transform of Fibonacci numbers

Combinatorics 2015-08-11 v1

Abstract

The generating function for the sequence A166861 in the OEIS (Euler transform of Fibonacci numbers) is Product_{k>0} 1/(1-x^k)^F(k), where F(k) are the Fibonacci numbers. This paper analyzes the more general generating function U(x) = Product_{k>0} 1/(1-x^k)^F(k+z), where z is a nonnegative integer, which provides asymptotics for the sequences A166861 (z=0), A200544 (z=1) and A260787 (z=2) in the OEIS.

Keywords

Cite

@article{arxiv.1508.01796,
  title  = {Asymptotics of the Euler transform of Fibonacci numbers},
  author = {Vaclav Kotesovec},
  journal= {arXiv preprint arXiv:1508.01796},
  year   = {2015}
}

Comments

7 pages, 1 figure