OrePolynomial[{{74933181*t^2 + 598503168*t^3 + 8758222848*t^4 + 
    10258219008*t^5 + 5049942016*t^6, {4}}, 
  {36*(8325909*t + 61387632*t^2 + 576064512*t^3 + 1606746112*t^4 + 
     1262485504*t^5), {3}}, 
  {60*(2775303 + 14967828*t + 67163904*t^2 + 942981120*t^3 + 1578106880*t^4), 
   {2}}, {120*(308367 + 8926848*t + 21639168*t^2 + 315621376*t^3), {1}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
