How would i show the following:

The number of partitions of the integer n into 3 parts is equal to the number of partitions of 2n into 3 parts of size less than n.

I've tried drawing the Ferrers diagram, but I can't seem to extract any useful information.

I am pretty sure the generating function for the number of partitions of the integer n into 3 parts is:

$\displaystyle (1+x+x^2+x^3+...)(1+x^2+x^4+x^6+...)(x^3+x^6+x^9+. ..) $

but I am not sure how to get the other generating function.

Thank you for your help.