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Fungrim entry: 071a94

s ⁣(n,k)=(−1)n+k[nk]s\!\left(n, k\right) = {\left(-1\right)}^{n + k} \left[{n \atop k}\right]
Assumptions:n∈Z≥0 and⁡ k∈Z≥0n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
s\!\left(n, k\right) = {\left(-1\right)}^{n + k} \left[{n \atop k}\right]

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
StirlingS1s ⁣(n,k)s\!\left(n, k\right) Signed Stirling number of the first kind
Powab{a}^{b} Power
StirlingCycle[nk]\left[{n \atop k}\right] Unsigned Stirling number of the first kind
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("071a94"),
    Formula(Equal(StirlingS1(n, k), Mul(Pow(-1, Add(n, k)), StirlingCycle(n, k)))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0)))))

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

2019-06-18 07:49:59.356594 UTC