{
  "id": "1009.4225",
  "version": "v4",
  "published": "2010-09-21T22:06:08.000Z",
  "updated": "2012-01-10T20:29:50.000Z",
  "title": "Two integer sequences related to Catalan numbers",
  "authors": [
    "Michel Lassalle"
  ],
  "comment": "15 pages, LaTeX, to appear in Journal of Combinatorial Theory, Series A",
  "journal": "Journal of Combinatorial Theory, Series A 119 (2012), 923-935",
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-01-10T20:29:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer sequences",
      "catalan number",
      "conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4225L"
    }
  }
}