What is the mathematical term for this? It's something like a factorial.
I honestly don't even know how to phrase this question, so let me demonstrate it with an example:
If the count is 1 then the formula is x = 1y
If the count is 2 then the formula is x = 1y + 2y
If the count is 3 then the formula is x = 1y + 2y + 3y
If the count is 4 then the formula is x = 1y + 2y + 3y + 4y
etc..
What is this called? And bonus question: is there a way to do this in Excel?
Factor out all the $y$'s and you get
$$x_n=y(1+2+3+\dots+n)=yT_n$$
where $T_n$ is a triangle number. We know that $T_n=\frac{n(n+1)}2$, thus,
$$x_n=\frac{yn(n+1)}2$$