"Motzkin number" meaning in English

{
  "etymology_text": "Named after Theodore Motzkin.",
  "forms": [
    {
      "form": "Motzkin numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Motzkin number (plural Motzkin 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 terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "For a given number n, the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). They have diverse applications in geometry, combinatorics, and number theory."
      ],
      "id": "en-Motzkin_number-en-noun-DN7k5f9e",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "intersect",
          "intersect"
        ],
        [
          "chord",
          "chord"
        ],
        [
          "point",
          "point"
        ],
        [
          "circle",
          "circle"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "number theory",
          "number theory"
        ]
      ],
      "raw_glosses": [
        "(mathematics) For a given number n, the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). They have diverse applications in geometry, combinatorics, and number theory."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Motzkin number"
      ]
    }
  ],
  "word": "Motzkin number"
}

{
  "etymology_text": "Named after Theodore Motzkin.",
  "forms": [
    {
      "form": "Motzkin numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Motzkin number (plural Motzkin 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 eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "en:Mathematics"
      ],
      "glosses": [
        "For a given number n, the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). They have diverse applications in geometry, combinatorics, and number theory."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "intersect",
          "intersect"
        ],
        [
          "chord",
          "chord"
        ],
        [
          "point",
          "point"
        ],
        [
          "circle",
          "circle"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "number theory",
          "number theory"
        ]
      ],
      "raw_glosses": [
        "(mathematics) For a given number n, the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). They have diverse applications in geometry, combinatorics, and number theory."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Motzkin number"
      ]
    }
  ],
  "word": "Motzkin number"
}