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This might be a super stupid question, but my math courses are long gone and I am stuck completely solving some math puzzles for fun. Just as a hobby, no homework involved.

I want to calculate the number of ways N coins can be partitioned. I have learned that there is an extra section of number theory for this and Euler was involved too, of course.

I can calculate the generalized pentagonal numbers using

$$ g_k = k(3k-1)/2 $$

but I have no clue how to calculate an actual value for $P(n)$. I see a lot of endless series but no solution. Could someone point to to some resources on how to work actually with these?

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marked as duplicate by Peter Taylor, Mostafa Ayaz, Vladhagen, Zubin Mukerjee, Shailesh Sep 25 '18 at 0:02

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