How many partitions do I have?
Mathematica, 11 bytes
PartitionsP
Explanation
¯\_(ツ)_/¯
Pyth, 3 bytes
l./
Try it here! or Try a test Suite.
The answer took much longer to format than writing the code itself :P.
How?
Pyth is the right tool for the job.
l./ Full program with implicit input. ./ Integer partitions. Return all sorted lists of positive integers that add to the input. l Length. Implicitly output the result.
Python 2, 85 83 bytes
-2 bytes thanks to @notjagan
lambda n:n<1or sum(sum(i*((n-k)%i<1)for i in range(1,n+1))*p(k)for k in range(n))/n
Try it online!
Using recursive formula from OEIS A000041.