OrePolynomial[{{-2*t + 121*t^2 + 475*t^3 - 1746*t^4 + 1152*t^5, {3}}, 
  {-4 + 514*t + 813*t^2 - 6372*t^3 + 4608*t^4, {2}}, 
  {296 - 432*t - 3204*t^2 + 2304*t^3, {1}}}, OreAlgebraObject[{Der[t]}, 
  Expand, #1 + #2 & , Expand[#1*#2] & , None], DegreeLexicographic]
