Partition generation

Calculus Level 5

Let the partition function \(P(n)\) enumerate the ways \(n\) can be expressed as a distinct sum of positive integers, eg \(P(4) = 5\) since \(4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1\) are the only ways to represent \(4\).

\[\prod_{p \ \text{prime}} \left[ \sum_{n=0}^{\infty} P(n)p^{-n} \right]\]

Does the above product converge?

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