"Catalan number" meaning in English

{
  "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": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "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": "quotation"
        },
        {
          "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 entries with language name categories using raw markup",
        "English entries with topic categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "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": "quotation"
        },
        {
          "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"
}