OrePolynomial[{{9*(198*t + 437*t^2 + 75*t^3 - 445*t^4 - 659*t^5 - 421*t^6 + 
     301*t^7 + 429*t^8 + 85*t^9), {4}}, 
  {18*(297 + 338*t - 1666*t^2 - 3414*t^3 - 1714*t^4 + 674*t^5 + 2658*t^6 + 
     2402*t^7 + 425*t^8), {3}}, 
  {4*(-3006 - 18757*t - 21055*t^2 + 14912*t^3 + 40906*t^4 + 41035*t^5 + 
     28855*t^6 + 4590*t^7), {2}}, 
  {4*(-2007 + 7670*t + 32635*t^2 + 39504*t^3 + 26353*t^4 + 16022*t^5 + 
     2295*t^6), {1}}}, OreAlgebraObject[{Der[t]}, Together, 
  Together[#1 + #2] & , Together[#1*#2] & , None], DegreeLexicographic]
