Two integer sequences related to Catalan numbers

Michel Lassalle

Two integer sequences related to Catalan numbers

Combinatorics 2012-08-01 v4

Authors: Michel Lassalle

Abstract

We prove the following conjecture of Zeilberger. Denoting by $C_n$ the Catalan number, define inductively $A_n$ by $(-1)^{n-1}A_n=C_n+\sum_{j=1}^{n-1} (-1)^{j} \binom{2n-1}{2j-1} A_j \,C_{n-j}$ and $a_n=2A_n/C_n$ . Then $a_n$ (hence $A_n$ ) is a positive integer.

Keywords

collatz conjecture number theory

Cite

@article{arxiv.1009.4225,
  title  = {Two integer sequences related to Catalan numbers},
  author = {Michel Lassalle},
  journal= {arXiv preprint arXiv:1009.4225},
  year   = {2012}
}

Comments

15 pages, LaTeX, to appear in Journal of Combinatorial Theory, Series A

Two integer sequences related to Catalan numbers

Abstract

Keywords

Cite

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