#OK to post homework
#Tianyi Liu,Sept 27, Assignment 6

1.
#Because in the procdure, it requires to calculate powerset of L which will easily get beyond computer's computational capability as L gets too large.
#[seq(PnxF(n,x),n=1..7)] and [seq(Pnx(n,x),n=1..7)] give same output.
#time([seq(Pnx(n,x),n=1..8)]); takes longer
#time([seq(PnxF(n,x),n=1..30)]); takes 0.15e-1
#It depends on how advanced the computer is, but normally it takes hours. 

2.
#x^0 represents the condition where there is no fixed points in the permutation. Its coefficient represents how many of these permuatitons exists, so its coefficient is always a constant. Since x^0=1, the coefficient times 1 will always be a constant term.

3.
#seq(coeff(PnxF(n,x),x,0),n=0..12):A000166
#seq(coeff(PnxF(n,x),x,1),n=0..12):No match
#seq(coeff(PnxF(n,x),x,2),n=0..12):A000387
#seq(coeff(PnxF(n,x),x,3),n=0..12):No match
#The largest i is 2.

4.
#a(n) = (n-1)*(a(n-1) + a(n-2))