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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).
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 ...
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Proving correspondence and partitions via generating functions, or at least I think so.
Let $A=\{2,6,10,14,\ldots\}$ be the set of integers that are twice an odd number.
Prove that, for every positive integer $n$, the number of partitions of $n$ in which no odd number appears more than ...
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