Very readable and simple. I like it.

Same as you, but I finally solved it after considering all the cases...

Sorry for the late reply, but you are absolutely right! Fixed now.

In the second example:

n = 4, k = 2 => [(1,4,2,3), (2,1,4,3), (3,1,2,4), (1,3,4,2), (2,3,4,1)] => 5

the last tuple (2,3,4,1) should have two inversions. I see three, i.e. (2,1), (3,1) and (4,1).

Shouldn't the last one be (2,3,1,4)?

Great kata! Getting the correct approach to solve it analytically didn't take that long but considering all the edge cases is pretty tedious. I don't even know if I managed to cover all of them.

Yeah you're right. Fiddled with this one for approx an hour before a solution just magically popped into my head. My naive implementation was waaayyy to slow but I somehow thought it was the only possible approach.
Now I can do n == 16 in a few seconds without running out of heap space.

Very nice Kata, took me quite some time.