code: def A_term(i,r,u,l1,l2,PAx,PBx,CPx,gamma):
      
      return pow(-1,i)*binomial_prefactor(i,l1,l2,PAx,PBx)*\
             pow(-1,u)*factorial(i)*pow(CPx,i-2*r-2*u)*\
             pow(0.25/gamma,r+u)/factorial(r)/factorial(u)/factorial(i-2*r-2*u)
docs: THO eq. 2.18
  
      >>> A_term(0,0,0,0,0,0,0,0,1)
      1.0
      >>> A_term(0,0,0,0,1,1,1,1,1)
      1.0
      >>> A_term(1,0,0,0,1,1,1,1,1)
      -1.0
      >>> A_term(0,0,0,1,1,1,1,1,1)
      1.0
      >>> A_term(1,0,0,1,1,1,1,1,1)
      -2.0
      >>> A_term(2,0,0,1,1,1,1,1,1)
      1.0
      >>> A_term(2,0,1,1,1,1,1,1,1)
      -0.5
      >>> A_term(2,1,0,1,1,1,1,1,1)    
      0.5