Given $X_1,...,X_n\sim Ber(p)$, I am interested in the distribution of the sum $L = \sum_{k=1}^n f_k X_k$ where $f_k$ are positive real numbers, not random. I have seen other posts such as this one and this one, where the last one gives probably the best answer to my question.
I would like to know if there is an explicit way of calculating the distribution of $L$ or, if not, what attempts have been made and why is it so hard to "find" it explicitly.