# Proof of the formula for the number of components in all partitions of a given number

I have to show that this formula is the number of components in all partitions of number $n$:

$$\sum_{i=1}^{n}\sum_{j=1}^{[n/i]}\sum_{k=0}^{n-ij}A_i(k) \cdot A_{j-1}(n-ij-k)$$ $A_k(n)$ is number of partitions $n$, that $k$ is the biggest possible number of components.

I have no idea how to start it. It is very difficult for me.