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Fungrim entry: 18ec99

s ⁣(n+1,k)=s ⁣(n,k1)ns ⁣(n,k)s\!\left(n + 1, k\right) = s\!\left(n, k - 1\right) - n s\!\left(n, k\right)
Assumptions:nZ0andkZ1n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 1}
TeX:
s\!\left(n + 1, k\right) = s\!\left(n, k - 1\right) - n s\!\left(n, k\right)

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
StirlingS1s ⁣(n,k)s\!\left(n, k\right) Signed 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("18ec99"),
    Formula(Equal(StirlingS1(Add(n, 1), k), Sub(StirlingS1(n, Sub(k, 1)), Mul(n, StirlingS1(n, k))))),
    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