Fungrim entry: 7774a3

\left[{n \atop k}\right] \le \frac{{2}^{n} n !}{k !}

Assumptions:

n \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`	$\left[{n \atop k}\right]$	Unsigned Stirling number of the first kind
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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)))))

Topics using this entry

Stirling numbers

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