I would like to determine the coefficient of a desired term in the product of two summation where the powers of $x$ are not necessarily integers. For example $$ \sum_{i=1}^N x^{1/i}\sum_{j=1}^N x^{1/j} $$ where $N=50$ is given. I want to know what is the coefficient of $x^{3/10}$ where I calculated just by $\texttt{Exp[ ]}$ command which is 4. Is there any direct and faster way to calculate such coefficients without expanding the product (as if $N$ increases, it would take a long time to expand it and also difficult to find the desired coefficient).
Thanks!