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

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- November 14th 2012, 11:34 AMI-Thinkgenerating functions, integer partitions
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