Add "partition number" `p(n)`

[inkydragon]

partition_num(n::Int) == length(integer_partitions(n::Int)) == length(partitions(n::Int))

Clean and export npartitions

https://github.com/JuliaMath/Combinatorics.jl/blob/edb9c2cba7240af0ca7f7b71164e269ed6868b7a/src/partitions.jl#L105-L124

ref:

• number of partitions of n - A000041 - OEIS
• NrPartitions(n) - GAP (ref) - Chapter 16: Combinatorics
• Partition Function P - MathWorld
• PartitionsP[n] — Wolfram