# Fungrim entry: f0d72c

$\left[{n + 1 \atop k}\right] = n \left[{n \atop k}\right] + \left[{n \atop k - 1}\right]$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}$
TeX:
\left[{n + 1 \atop k}\right] = n \left[{n \atop k}\right] + \left[{n \atop k - 1}\right]

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
StirlingCycle$\left[{n \atop k}\right]$ Unsigned Stirling number of the first kind
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("f0d72c"),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(1)))))