I know that integers can be partitioned into the different ways to get that integer. For example:
$$4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1$$
can be written as
$$(4),(3, 1),(2, 2),(2, 1, 1), (1, 1, 1, 1)$$
We can then define the size of a partition
$$λ = (λ_1, \ldots, λ_k)$$
to be
$$\sum λ_i$$ (so partitions of $n$ have size $n$)
How can I find a generating function for the set of all integer partitions?