#please do not post homework
Kenneth Chan
Math 454
HW 11

1.2048*32=65536,
n=number of dolls and k= number of tower
X=the sum of k=0 to n of the binomial n over k multiplied by the sum of i=0 to k of the binomial of k over i

2.xn(x,n)=>seq(add(nops(x-(y-1),y=1..n)))
Axn(x,n)=>Sum(Snk(n,k)*xn(x,k),k=0..n)

3. We can shove recurrence relation by using the terms of permuatation with k cycles.
We can add na new object and instead of using n-1 we replace it with n with k cycles.
to form a new permuation of n+1 objects and k cycles one must insert the a new variable into 
this list and there are n ways to do the action. This will gives us n *the binimial of n over k term of the recurrence relation.

4.
cnk:=proc(n,k) 
option remember:
if k<1 then
Return(0):
fi:
if k>n then
Return(1):
fi:
cnk(n-1,k-1)+(n-1)*cnk(n-1,k):
end:

5. Σk=1 to n( Σk=1 to (n-1))*x^kno clue what im supposed to do here