"Touchard polynomial" meaning in English

{
  "etymology_text": "Studied by Jacques Touchard.",
  "forms": [
    {
      "form": "Touchard polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Touchard polynomial (plural Touchard polynomials)",
      "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": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿ"
      ],
      "id": "en-Touchard_polynomial-en-noun-LHo6xANt",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "binomial",
          "binomial"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿ"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Jacques Touchard",
        "Touchard polynomial"
      ]
    }
  ],
  "word": "Touchard polynomial"
}

{
  "etymology_text": "Studied by Jacques Touchard.",
  "forms": [
    {
      "form": "Touchard polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Touchard polynomial (plural Touchard polynomials)",
      "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",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿ"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "binomial",
          "binomial"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿ"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Jacques Touchard",
        "Touchard polynomial"
      ]
    }
  ],
  "word": "Touchard polynomial"
}