An unrestricted partition (order does not count, equality of sizes is ok) partition is called self-conjugate if it is identical with its conjugate. E. g 8 = 4 + 2 + 1 + 1.

Show that the number of self conjugate unrestricted partitions of n is equal to the number of partitions of n into distinct odd parts

(optional) express this result as an identity of generating functions.