This is from a math contest. I have solved it, but I'm posting it on here because I think that it would be a good challange problem for precalculus courses. Also, it's kind of fun.
Write the polynomial $ \prod_{n=1}^{1996}(1+nx^{3^n})$=$\sum_{n=0}^m a_nx^{k_n}$, where the $k_n$ are in increasing order, and the $a_n$ are nonzero. Find the coefficent $a_{1996}$.