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Fungrim entry: 9fbe4f

{n+1k}=k{nk}+{nk−1}\left\{{n + 1 \atop k}\right\} = k \left\{{n \atop k}\right\} + \left\{{n \atop k - 1}\right\}
Assumptions:n∈Z≥0  and⁡  k∈Z≥1n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}
TeX:
\left\{{n + 1 \atop k}\right\} = k \left\{{n \atop k}\right\} + \left\{{n \atop k - 1}\right\}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
StirlingS2{nk}\left\{{n \atop k}\right\} Stirling number of the second kind
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("9fbe4f"),
    Formula(Equal(StirlingS2(Add(n, 1), k), Add(Mul(k, StirlingS2(n, k)), StirlingS2(n, Sub(k, 1))))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(1)))))

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2021-03-15 19:12:00.328586 UTC