Question

Let p n (resp. P n ) be the set of partitions of n with all parts odd (resp. Even). Show that x odd 2n p 1 x p 2n even 1 (2n 1)!! Z = z = , (2n)!! Where the double factorial is dened by n!! = n(n 2) . . . With lower limit 1 or 2 depending on the parity of n.

Answer 1

Map every part xi of 2n to xi/2.