I miss Mathematica

Why? Because Mathics is not up to helping me determine if indeed
f({A1,,Ap})=(np)!2n!p!(1p)np|A1|2|Ap|2|A1|!|Ap|!


is a pmf over the set of partitions of the set {1,,n} into pn nonempty sets. In particular, the sets A1,,Ap in the formula above satisfy |A1|++|Ap|=n and |Ai|1 for all i.

I feel like I could empirically test this easily in Mathematica, but OMG trying to do it in Matlab is a real pain, so I gave up. Combinatorics or set manipulation in Matlab in general is an exercise in trying to make a smoothie with a grater: you can do it, eventually, but it’s going to take forever and make a mess.