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Question 1:
By iterating procedure CP(L1,L2), in
M12.txt

write a procedure

CPg(L)

that inputs a list of lists L=[L1,L2, ...,Lk] of "databases" (represented as lists L1, L2, ..., Lk) and outputs

CP(L1,L2, ..., Lk)

In particular, CPg([L1,L2]) should output the same as CP(L1,L2) for any two lists of integers L1 and L2

CPg:=proc(L) local l1, i:
option remember:
if nops(L) = 0 then:
return('FAIL'):
fi:
l1:=[0]:
for i in L do:
l1:=CP(l1,i):
end: 
l1
end proc:

Question 2:

Procedures AveClever(L) and kthMomentClever(L,k) inputs a database L, and first finds its weight-enumerator. Suppose that you already know the weight-enumerator, call it f, in the variable x. Modify these procedures to write procedures
AveGF(f,x) and kthMomentGF(f,x,k)

that do the same things if you already have the weight-enumerator f (in terms of x).

In particular, for any "data-base" L, check that

AveGF(WtEn(L,x),x)= AveClever(L)

and

kthMomentGF(WtEn(L,x),x,k)= kthMomentClever(L,k)

Answer 2:
AveGF:=proc(f, x):
subs(x=1,diff(f,x))/subs(x=1,f):
end proc:

kthMomentGF:=proc(f,x,k) local mu,f1,i:
mu:=AveGF(f,x):
f1:=f/x^mu/subs(x=1,f):
for i from 1 to k do
f1:=expand(x*diff(f1,x)):
od:
subs(x=1,f1):
end:

Question 3:
ScaledMomentGF:=proc(f, x, k) local l1, l2, ans:
l1:=kthMomentGF(f, x, k):
ans:=k/2:
l2:=kthMomentGF(f, x, 2)^ans:
l1/l2
end proc:

Question 4:

seq(limit(ScaledMomentGF(((1+x)/2)^n,x,k), n=infinity), k=2..20)
1, 0, 3, 0, 15, 0, 105, 0, 945, 0, 10395, 0, 135135, 0, 2027025, 

  0, 34459425, 0, 654729075
#A123023 is the OEIS number for the above sequence