"exponential generating function" meaning in English

{
  "forms": [
    {
      "form": "exponential generating functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "exponential generating function (plural exponential generating functions)",
      "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",
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "Exponential generating functions are generally more convenient than ordinary generating functions for combinatorial enumeration problems that involve labelled objects.",
          "type": "example"
        }
      ],
      "glosses": [
        "A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied."
      ],
      "hypernyms": [
        {
          "word": "generating function"
        }
      ],
      "id": "en-exponential_generating_function-en-noun-XI5YNbqR",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "formal power series",
          "formal power series"
        ],
        [
          "coefficient",
          "coefficient"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "exponential generating function"
}

{
  "forms": [
    {
      "form": "exponential generating functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "exponential generating function (plural exponential generating functions)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "generating function"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with usage examples",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "Exponential generating functions are generally more convenient than ordinary generating functions for combinatorial enumeration problems that involve labelled objects.",
          "type": "example"
        }
      ],
      "glosses": [
        "A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied."
      ],
      "links": [
        [
          "mathematics",
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        ],
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          "formal power series",
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        ],
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          "coefficient",
          "coefficient"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "exponential generating function"
}