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Fungrim entry: f0d72c

[n+1k]=n[nk]+[nk1]\left[{n + 1 \atop k}\right] = n \left[{n \atop k}\right] + \left[{n \atop k - 1}\right]
Assumptions:nZ0andkZ1n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 1}
TeX:
\left[{n + 1 \atop k}\right] = n \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
StirlingCycle[nk]\left[{n \atop k}\right] Unsigned Stirling number of the first kind
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("f0d72c"),
    Formula(Equal(StirlingCycle(Add(n, 1), k), Add(Mul(n, StirlingCycle(n, k)), StirlingCycle(n, Sub(k, 1))))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(1)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-11-11 15:50:15.016492 UTC