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Fungrim entry: 512beb

Bn≤(0.792nlog⁡ ⁣(n+1))nB_{n} \le {\left(\frac{0.792 n}{\log\!\left(n + 1\right)}\right)}^{n}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
B_{n} \le {\left(\frac{0.792 n}{\log\!\left(n + 1\right)}\right)}^{n}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Powab{a}^{b} Power
Loglog⁡(z)\log(z) Natural logarithm
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("512beb"),
    Formula(LessEqual(BellNumber(n), Pow(Div(Mul(Decimal("0.792"), n), Log(Add(n, 1))), n))),
    Variables(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