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Fungrim entry: 255576

k=0n{nk}=Bn\sum_{k=0}^{n} \left\{{n \atop k}\right\} = B_{n}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} \left\{{n \atop k}\right\} = B_{n}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
StirlingS2{nk}\left\{{n \atop k}\right\} Stirling number of the second kind
BellNumberBnB_{n} Bell number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("255576"),
    Formula(Equal(Sum(StirlingS2(n, k), Tuple(k, 0, n)), BellNumber(n))),
    Variables(n),
    Assumptions(Element(n, 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.

2019-08-25 15:30:03.056001 UTC