All of this happened so long ago for me, things are a little rusty. I’m calling this a partial factorial because I don’t know what else to call it.
What is the notation for a product of the form:
n • (n-1) • (n-2) • … • (n-r+1)
For example:
n=12, r=6: 12 • 11 • 10 • 9 • 8 • 7
I know that it can be calculated as
$\frac{n!}{(r)!}$
but I wondered whether there is a notation similar to that for combinations or permutations.
I am aware that I can write it as:
$\prod_{i=1}^r n-i+1$
but that’s not very compact.
Best Answer
You might be thinking of the falling factorial, usually denoted $ n^{\underline{r}} $ or $ (n)_r $, where
$$ n^{\underline{r}} := n(n-1)(n-2)\cdots(n-r+1). $$