15. An unconventional pair of dice is constructed as follows: the first one has its faces labeled 4, 3, 3, 2, 2, 1, and the second is labeled 8, 6, 5, 4, 3, 1. Identify the generating function where the coefficient of $x^k$ tells us how many ways we can roll a sum of $k$ using this pair of weird dice. Using a computer to expand, what do you notice? (If you don't see it, consider normal dice).
