Provide a generic formula for the number of partitions of an even number $~n~$ where one part has even value and another part also has even value.
Is there some way to approach this problem that uses Generating Functions?
2026-03-25 23:37:16.1774481836
Integer Partitions of $~n~$ with restrictions.
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Hint. The generating function of the number of partitions with at least two even parts is $$\prod_{k=1}^{\infty}\frac{1}{1-x^k}-\frac{1}{1-x^2}\cdot\prod_{k=1}^{\infty}\frac{1}{1-x^{2k-1}}=x^4+x^5+3x^6+4x^7+8x^8+11x^9+\dots$$