#Homework by Mike Murr
#OK to post
#hw8

read(`C8.txt`);

SPnF:=proc(n) local S, n1, SP1, i, S1, S2, n2, i2, chosen, chosenplus;

if n=0 then
  return({{}});
fi;

if n = 1 then
  return({{1}});
fi;

SP1:={};

S:=SPnF(n-1);

n1:=nops(S);
print(n1);

for i from 1 to n1 do
  S2:=convert(S, list);
  S1:=S2[i];
#  print(S1);
  if n=2 then
    SP1:=SP1 union {{{n} union S1}};
    SP1:=SP1 union {{{n}, S1}};
  else
    SP1:=SP1 union {{{n} union S1[]}};
#    print(SP1);
    SP1:=SP1 union {{{n}, S1[]}};
#    print(SP1);
    n2 :=nops(S1);
    if n2 >= 2 then
      for i2 from 1 to n2 do
        chosen:=S1[i2];
        chosenplus :={chosen union {n}};
        SP1:=SP1 union {S1[1..i2-1] union S1[i2+1..n2] union chosenplus };
      end do;
     fi;
  end if;
end do;

return(SP1);

end proc;

SPnF(0);
SPnF(1);
SPnF(2);
SPnF(3);
SPnF(4);

# Exercise 3
# 
# 

expansion := taylor(log(Sum(2^(n*(n-1)/2)*x^n/n!,n=0..infinity)),x=0,31);
expansion;

seq(i!*coeff(expansion,x,i),i=1..30);

# In the OEIS it is A001187