Partition

Let $n$ be an integer. Let $p(0)=1$ and let $p(n)=0$ for negative $n$. For positive $n$, the partition function $p(n)$ is the number of possible partitions of a number $n$ into sums of natural numbers.

Example: We see that $p(4)=5$ because we can write $$\begin{array}{ll} 4 &= 1+3 \\ &= 1+1+2 \\ &= 1+1+1+1 \\ &= 2+2 \\ &= 0+4 \end{array}$$