I'm doing a problem about arranging people into groups, and having watched Numberphile's video on partitions recently, I'm trying to use partitions to solve it.
Is there any way to find the number of partitions which have a certain number of elements?
For example, one can sum to $4$ in only one way using 3 positive integers: $\{2, 1, 1\}$.
Is there any way to find the number of ways of doing this for numbers $n \leq 20$?
Thank you.