Evaluate $\prod_{k=1}^{n} \sum_{i\ =1}^{k} a_i$ in $\mathcal{O}(n)$

Write a Matlab program, which takes the vector $$(a_1, \ldots, a_n)$$ and outputs $$\prod_{k=1}^{n} \sum_{i\ =1}^{k} a_i$$. You are only allowed to define two variables and have to solve the problem in $$\mathcal{O}(n)$$.

I am pretty sure this is closely related to Horner’s method, but I haven’t been able to simplify the expression for small $$n$$ into a form that looked like Horner.

Any help is appreciated 🙂