I am trying to do Project Euler #78, which is about the different ways of splitting up coins into piles. I realized that this is just the number of integer partitions of the number of coins, specifically the Partition Function P. I am having trouble figuring out what the MathWorld page on the subject means for a generating function. I know it has to do with a polynomial and pentagonal number powers. Here is the generating function it gives:
I would greatly appreciate if someone who understands this could help explain it to me and maybe give a worked out example for some small numbers. Thanks!