I have been stuck in this problem and have no idea of how to solve it. I have a hint from the book but don't really see how to use it. Any suggestion or hint would be really appreciated. Thanks!
Show that there is a constant $c$ such that if $f(n)$ is the number of solutions $2x+3y+5z=n$ in nonnegative integers, then $f(n) \sim cn^2$. Find the value of $c$. The hint tells me to work with $\sum_nf(n)x^n= \frac{1}{(1-x^2)(1-x^3)(1-x^5)}$, expand the terms and write it using partial fractions.