"binomial coefficient" meaning in All languages combined

{
  "forms": [
    {
      "form": "binomial coefficients",
      "tags": [
        "plural"
      ]
    }
  ],
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    {
      "args": {},
      "expansion": "binomial coefficient (plural binomial coefficients)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "kind": "other",
          "name": "Terms with Icelandic translations",
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        },
        {
          "kind": "other",
          "name": "Terms with Serbo-Croatian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Combinatorics",
          "orig": "en:Combinatorics",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        }
      ],
      "glosses": [
        "a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as \"n choose k\""
      ],
      "id": "en-binomial_coefficient-en-noun-AIPxib0T",
      "links": [
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "binomial",
          "binomial"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as \"n choose k\""
      ],
      "topics": [
        "combinatorics",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "cs",
          "lang": "Czech",
          "sense": "binomial coefficient",
          "tags": [
            "neuter"
          ],
          "word": "kombinační číslo"
        },
        {
          "code": "da",
          "lang": "Danish",
          "sense": "binomial coefficient",
          "tags": [
            "common-gender"
          ],
          "word": "binomialkoefficient"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "binomial coefficient",
          "word": "binomikerroin"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "binomial coefficient",
          "tags": [
            "masculine"
          ],
          "word": "coefficient binomial"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "binomial coefficient",
          "tags": [
            "masculine"
          ],
          "word": "Binomialkoeffizient"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "binomial coefficient",
          "word": "binomiális együttható"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "binomial coefficient",
          "tags": [
            "masculine"
          ],
          "word": "tvíliðustuðull"
        },
        {
          "code": "sh",
          "lang": "Serbo-Croatian",
          "sense": "binomial coefficient",
          "tags": [
            "masculine"
          ],
          "word": "binomni koeficijent"
        }
      ]
    }
  ],
  "word": "binomial coefficient"
}

{
  "forms": [
    {
      "form": "binomial coefficients",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
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      "expansion": "binomial coefficient (plural binomial coefficients)",
      "name": "en-noun"
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English entries with incorrect language header",
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        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Czech translations",
        "Terms with Danish translations",
        "Terms with Finnish translations",
        "Terms with French translations",
        "Terms with German translations",
        "Terms with Hungarian translations",
        "Terms with Icelandic translations",
        "Terms with Serbo-Croatian translations",
        "en:Combinatorics"
      ],
      "glosses": [
        "a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as \"n choose k\""
      ],
      "links": [
        [
          "combinatorics",
          "combinatorics"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "binomial",
          "binomial"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as \"n choose k\""
      ],
      "topics": [
        "combinatorics",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "binomial coefficient",
      "tags": [
        "neuter"
      ],
      "word": "kombinační číslo"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "binomial coefficient",
      "tags": [
        "common-gender"
      ],
      "word": "binomialkoefficient"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "binomial coefficient",
      "word": "binomikerroin"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "binomial coefficient",
      "tags": [
        "masculine"
      ],
      "word": "coefficient binomial"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "binomial coefficient",
      "tags": [
        "masculine"
      ],
      "word": "Binomialkoeffizient"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "binomial coefficient",
      "word": "binomiális együttható"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "binomial coefficient",
      "tags": [
        "masculine"
      ],
      "word": "tvíliðustuðull"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "binomial coefficient",
      "tags": [
        "masculine"
      ],
      "word": "binomni koeficijent"
    }
  ],
  "word": "binomial coefficient"
}