1. PIE is inefficient for large numbers of sets because it gets exponentially larger, which becomes slow.

[seq(Pnx(n,x),n=1..7)] is equal to [seq(PnxF(n,x),n=1..7)]

time([seq(PnxF(n, x),n=1..8)]) is less than time([seq(Pnx(n,x),n=1..8)])

time([seq(Pnx(n,x),n=1..8)]) = .328 and time([seq(PnxF(n,x),n=1..8)]) = 0
Pnx(n,x) takes longer.

2. D(n) represents the number of permutations of the n objects with 0 fixed points, or the number of derangements of n objects. This must be constant, since it is fixed.


3. 
i=0: A000166
i=1: A182390
i=2: A000387
i=3: Does not exist
i=4: Does not exist
i=2 is the largest for which there is a sequence

4.
d(n)=(n-1)*(d(n-1)+d(n-2))