30*(27000000000 + 84037500000*z - 346865625000*z^2 - 55567000000*z^3 + 
   187923165625*z^4 + 36477006875*z^5 + 21336230625*z^6 + 19123388575*z^7 + 
   6925739310*z^8 + 1443544710*z^9 + 163913184*z^10 + 7525440*z^11)*P[z] + 
 10*(-189000000000 + 4816462500000*z - 7268326875000*z^2 - 
   21210430812500*z^3 + 2664478321875*z^4 + 3711617481250*z^5 - 
   135661728250*z^6 + 689643286650*z^7 + 607021304825*z^8 + 
   209673119160*z^9 + 40678130502*z^10 + 4143853440*z^11 + 167064768*z^12)*
  Derivative[1][P][z] + 5*(-3240000000000 + 5055750000000*z + 
   44457862500000*z^2 - 133825053750000*z^3 - 110925736437500*z^4 + 
   13367806743750*z^5 - 6199228765625*z^6 - 8282515456375*z^7 + 
   1646226060075*z^8 + 2287368823475*z^9 + 810956145330*z^10 + 
   149186684934*z^11 + 13819981248*z^12 + 496679040*z^13)*
  Derivative[2][P][z] + 5*z*(-13162500000000 + 45343125000000*z + 
   40530375000000*z^2 - 190176960000000*z^3 - 77498059625000*z^4 - 
   3649915059375*z^5 - 26918293320000*z^6 - 13545524756500*z^7 - 
   465440555100*z^8 + 1350059072325*z^9 + 524857986060*z^10 + 
   92744995638*z^11 + 7892060544*z^12 + 255864960*z^13)*Derivative[3][P][z] + 
 10*z^2*(-5568750000000 + 23905125000000*z + 3393646875000*z^2 - 
   39702348750000*z^3 - 7716298734375*z^4 - 3779011321875*z^5 - 
   7801785421250*z^6 - 3351125770500*z^7 - 382134335775*z^8 + 
   148313757125*z^9 + 68439921540*z^10 + 11725276842*z^11 + 923795772*z^12 + 
   27279720*z^13)*Derivative[4][P][z] + 
 8*z^3*(5 + z)*(-354375000000 + 1774828125000*z - 503550000000*z^2 - 
   1289447109375*z^3 + 254876515625*z^4 - 266627903125*z^5 - 
   304623830625*z^6 - 87265479875*z^7 - 4878146975*z^8 + 3939663705*z^9 + 
   1048560285*z^10 + 97471734*z^11 + 3057210*z^12)*Derivative[5][P][z] + 
 16*(-5 + z)*(-1 + z)*z^4*(5 + z)^2*(10 + z)*(15 + z)*(5 + 3*z)*
  (-675000 + 3465000*z - 1053375*z^2 + 933650*z^3 + 449735*z^4 + 144776*z^5 + 
   15678*z^6)*Derivative[6][P][z]
