V:=Vector([1,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11]):

S:=V[2]^2-4*V[3]:

for N from 3 to 11 do

  T:=V[N]^2*S:
  S:=T:

  for K from 1 to N-1 do
    U:=(-N)*diff(T,V[2]):
    for J from 2 to N-1 do
      U:=U+((J-(N+1))*V[J])*diff(T,V[J+1]):
    end do:
    divide(U,K*V[N],'T'):
    S:=S+T*V[N+1]^K:
  end do:

  S:=expand(S):
  print(nops(S)):
end do:

quit: