Implement the partition function – mathematica.stackexchange.com

I am trying to write my own version of the PartitionsP function. Here is my code P[1, 1] = 1; P[n_, k_] := With[{x = n - k}, If[x == 0, 1, If[x <= k, Sum[P[x, i], {i, 1, x}], Sum[P[x, i], ...

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