I'm working on a partition problem, and I got an answer that is simply staggering, and I was hoping for someone to verify whether my answer is correct.
The question was simply to determine the number of partitions of 200 into at most 6 parts. I know that the partition of $n$ into at most $k$ parts is equivalent to the partition of $n$ into parts of size at most $k$, so I created a generating function that looks like this:
$$g(t)=(1+t^{1}+t^{2}+t^{3}+...+t^{200})(1+t^{2}+t^{4}+...+t^{200})...(1+t^{6}+t^{12}+...+t^{198})$$
Then used software to expand and find the coefficient of $t^{200}$.
I got an answer of $4,775,383$. Can someone please verify this? I can kind of believe it, but it's a figure I certainly wasn't expecting!
Thanks for your time!