OGF for partitions of integer r-N into even parts less than or equal to 2m (N is some integer that may depend on m).

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Let $a_r$ be the number of partitions of the integer r-N into even parts, the largest of which is less than or equal to 2m, where N is some integer that may depend on m. Find the ordinary generative function for the sequence {$a_0$,$a_1$,$a_2$,...,$a_r$,...}.

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