12*z*(256 + 632*z + 702*z^2 + 382*z^3 + 98*z^4 + 9*z^5)*P[z] + 
 12*(-384 + 224*z + 3716*z^2 + 7633*z^3 + 6734*z^4 + 2939*z^5 + 604*z^6 + 
   45*z^7)*Derivative[1][P][z] + 
 6*z*(-5376 - 5248*z + 11080*z^2 + 25286*z^3 + 19898*z^4 + 7432*z^5 + 
   1286*z^6 + 81*z^7)*Derivative[2][P][z] + 
 2*z^2*(4 + 3*z)*(-3456 - 2304*z + 3676*z^2 + 4920*z^3 + 2079*z^4 + 356*z^5 + 
   21*z^6)*Derivative[3][P][z] + (-1 + z)*z^3*(2 + z)*(3 + z)*(6 + z)*(8 + z)*
  (4 + 3*z)^2*Derivative[4][P][z]
