{
  "id": "0712.3946",
  "version": "v1",
  "published": "2007-12-23T20:12:32.000Z",
  "updated": "2007-12-23T20:12:32.000Z",
  "title": "A combinatorial interpretation for the identity Sum_{k=0}^{n} binom{n}{k} Sum_{j=0}^{k} binom{k}{j}^{3}= Sum_{k=0}^{n} binom{n}{k}^{2}binom{2k}{k}",
  "authors": [
    "David Callan"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The title identity appeared as Problem 75-4, proposed by P. Barrucand, in Siam Review in 1975. The published solution equated constant terms in a suitable polynomial identity. Here we give a combinatorial interpretation in terms of card deals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-23T20:12:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "combinatorial interpretation",
      "published solution equated constant terms",
      "title identity",
      "suitable polynomial identity",
      "card deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3946C"
    }
  }
}