Factorial, but with addition [duplicate]
Is there a notation for addition form of factorial?
$$5! = 5\times4\times3\times2\times1$$
That's pretty obvious. But I'm wondering what I'd need to use to describe
$$5+4+3+2+1$$
like the factorial $5!$ way.
EDIT: I know about the formula. I want to know if there's a short notation.
Solution 1:
It is called the $n$th triangle number and it can be written as $\binom{n+1}2$, as a binomial coefficient.
Solution 2:
That can be done with the formula $\frac{n^2+n}{2}$