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Fungrim entry: 4b65d0

Bn=k=1nknk!j=0nk(1)jj!B_{n} = \sum_{k=1}^{n} \frac{{k}^{n}}{k !} \sum_{j=0}^{n - k} \frac{{\left(-1\right)}^{j}}{j !}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
B_{n} = \sum_{k=1}^{n} \frac{{k}^{n}}{k !} \sum_{j=0}^{n - k} \frac{{\left(-1\right)}^{j}}{j !}

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(BellNumber(n), Sum(Mul(Div(Pow(k, n), Factorial(k)), Sum(Div(Pow(-1, j), Factorial(j)), For(j, 0, Sub(n, k)))), For(k, 1, n)))),
    Assumptions(Element(n, 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.

2021-03-15 19:12:00.328586 UTC