{
  "id": "0709.2947",
  "version": "v1",
  "published": "2007-09-19T03:36:21.000Z",
  "updated": "2007-09-19T03:36:21.000Z",
  "title": "Sums of Products of Bernoulli numbers of the second kind",
  "authors": [
    "Ming Wu",
    "Hao Pan"
  ],
  "comment": "Accepted by the Fibonacci Quarterly",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "The Bernoulli numbers b_0,b_1,b_2,.... of the second kind are defined by \\sum_{n=0}^\\infty b_nt^n=\\frac{t}{\\log(1+t)}. In this paper, we give an explicit formula for the sum \\sum_{j_1+j_2+...+j_N=n, j_1,j_2,...,j_N>=0}b_{j_1}b_{j_2}...b_{j_N}. We also establish a q-analogue for \\sum_{k=0}^n b_kb_{n-k}=-(n-1)b_n-(n-2)b_{n-1}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-19T03:36:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "05A19"
    ],
    "keywords": [
      "bernoulli numbers",
      "second kind",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2947W"
    }
  }
}