Factorial, but with addition

It is called the $n$th triangle number and it can be written as $\binom{n+1}2$, as a binomial coefficient.

That can be done with the formula $\frac{n^2+n}{2}$

We should also note that the factorial function has a similar look to it as the sigma summation notation; as $$\frac{n(n+1)}{2}=1+2+3+...+n=\sum_{k=1}^nk$$ $$n!=1 \cdot 2 \cdot 3 \cdot ... \cdot n=\prod_{k=1}^nk$$