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Fungrim entry: 7774a3

[nk]2nn!k!\left[{n \atop k}\right] \le \frac{{2}^{n} n !}{k !}
Assumptions:nZ0andkZ0n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
StirlingCycle[nk]\left[{n \atop k}\right] Unsigned Stirling number of the first kind
Powab{a}^{b} Power
Factorialn!n ! Factorial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("7774a3"),
    LessEqual(StirlingCycle(n, k), Div(Mul(Pow(2, n), Factorial(n)), Factorial(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.

2019-10-05 13:11:19.856591 UTC