"Catalan number" meaning in All languages combined

{
  "etymology_text": "Named after the Belgian mathematician Eugène Catalan (1814–1894).",
  "forms": [
    {
      "form": "Catalan numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Catalan number (plural Catalan numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Combinatorics",
          "orig": "en:Combinatorics",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 2013-04-19:",
          "text": "AMBIGUITY LEADS TO AN EXPONENTIAL NUMBER OF TREES\nI saw the man with the telescope on the box in the car under the table ...\nn prepositional phrases ⇒ (n + 1)’th catalan number",
          "type": "quote"
        },
        {
          "text": "Cₙ — the nᵗʰ Catalan number — could be described as the number of distinct ways in which a sequence of n + 1 numbers could be associated by means of some specified binary operator."
        }
      ],
      "glosses": [
        "In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the nᵗʰ Catalan number is equal to (2n choose n) over (n+1)."
      ],
      "id": "en-Catalan_number-en-noun-fTdyhSkp",
      "links": [
        [
          "combinatorial",
          "combinatorial"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "recursive",
          "recursive"
        ],
        [
          "choose",
          "choose"
        ]
      ],
      "wikipedia": [
        "Catalan number"
      ]
    }
  ],
  "word": "Catalan number"
}

{
  "etymology_text": "Named after the Belgian mathematician Eugène Catalan (1814–1894).",
  "forms": [
    {
      "form": "Catalan numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Catalan number (plural Catalan numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Combinatorics"
      ],
      "examples": [
        {
          "ref": "1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 2013-04-19:",
          "text": "AMBIGUITY LEADS TO AN EXPONENTIAL NUMBER OF TREES\nI saw the man with the telescope on the box in the car under the table ...\nn prepositional phrases ⇒ (n + 1)’th catalan number",
          "type": "quote"
        },
        {
          "text": "Cₙ — the nᵗʰ Catalan number — could be described as the number of distinct ways in which a sequence of n + 1 numbers could be associated by means of some specified binary operator."
        }
      ],
      "glosses": [
        "In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the nᵗʰ Catalan number is equal to (2n choose n) over (n+1)."
      ],
      "links": [
        [
          "combinatorial",
          "combinatorial"
        ],
        [
          "mathematics",
          "mathematics"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "recursive",
          "recursive"
        ],
        [
          "choose",
          "choose"
        ]
      ],
      "wikipedia": [
        "Catalan number"
      ]
    }
  ],
  "word": "Catalan number"
}