Fungrim home page

Fungrim entry: ea9e2f

∑k=0n[nk]=n!\sum_{k=0}^{n} \left[{n \atop k}\right] = n !
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} \left[{n \atop k}\right] = n !

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sum∑nf(n)\sum_{n} f(n) Sum
StirlingCycle[nk]\left[{n \atop k}\right] Unsigned Stirling number of the first kind
Factorialn!n ! Factorial
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("ea9e2f"),
    Formula(Equal(Sum(StirlingCycle(n, k), For(k, 0, n)), Factorial(n))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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