Show the number of partitions of n in which only odd parts may be repeated equals the number of partitions of n in which no part appears more than three times

Answer 1

Take a look here:

http://math.stackexchange.com/questions/54961/the-number-of-partitions-of-n-into-distinct-parts-equals-the-number-of-partiti

and I think you will see how to build the proof you want.