Ã -- gedei ( 1186-1241 ) was the third son of Genghis Khan and second Great Khan of the Mongol Empire , after his father . Ã -- gedei Khan ( , Ã -- gedei ; also Ogotai or Oktay ; Ogodei ) ( c. 1186 â `` December 11 , 1241 ) was the third son of Genghis Khan and second Great Khan ( Khagan ) of the Mongol Empire by succeeding his father .