Additional Info: The number of partitions of a number $n$ can be found out using the following diagram:
\begin{array}{c c c c c} \color{red}{1}\\ 1 &\color{red}{2}\\ 2 &3 &\color{red}{5}\\ 5 &7 &10 &\color{red}{15} \cdots \end{array}
The number of ways a set of $n$ elements can be partitioned into nonempty subsets is called a Bell number and can be obtained by constructing a triangle as above. The first row starts with a $1$. For the first element of next row you copy the last element of previous row. And find the sum with number above and right it in the next column, till $n^{th}$ row having $n$ elements.