Just want to make sure this is correct

Supposed to construct the generating function for the set of all integer partitions such that each even part is divisible by 4 and each odd part occurs an even number of times.

Came up with

$\displaystyle \prod_{m=1}^{\infty}\frac{1}{1-x^{4m}}\prod_{n=1}^{\infty}\frac{1}{1-x^{2(2n-1)}}$