{
  "id": "1508.01796",
  "version": "v1",
  "published": "2015-08-07T19:24:45.000Z",
  "updated": "2015-08-07T19:24:45.000Z",
  "title": "Asymptotics of the Euler transform of Fibonacci numbers",
  "authors": [
    "Vaclav Kotesovec"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-07T19:24:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "41A60",
      "11B39",
      "05A15"
    ],
    "keywords": [
      "fibonacci numbers",
      "euler transform",
      "asymptotics",
      "sequence a166861",
      "sequences a166861"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}