Carloman of Bavaria was the eldest grandson of what descendant of Charlemagne?
Carloman of Bavaria Carloman (German: "Karlmann" , Latin: "Karlomannus" ; c. 830 – 22 March 880), was a Frankish king of the Carolingian dynasty. He was the eldest son of Louis the German, king of East Francia, and Hemma, daughter of a Bavarian count. His father appointed him margrave of Pannonia in 856, and upon his father's death in 876 he became King of Bavaria. He was appointed by King Louis II of Italy as his successor, but the Kingdom of Italy was taken by his uncle Charles the Bald in 875. Carloman only conquered it in 877. In 879 he was incapacitated, perhaps by a stroke, and abdicated Bavaria to Louis the Younger and Italy to Charles the Fat.
Arnulf of Sens Arnulf of Sens(ca.794 - April, 841) was a Frankish noble, an illegitimate son of the 16 year old Prince Louis the Pious, the son of the Carolingian King Charlemagne (who would be crowned emperor in 800). His mother Theodelinde of Sens (ca.764 - 794), was 30 years old and was the daughter of Gainfroi, count of Sens and Theidlindis de Blois. He had one sister, Alpaïs de Paris, abbess of St-Pierre de Reims. In 794 A.D., Arnulf's mother Theodelinde of Sens was dead. His grandfather Charlemange died in 814 at age 72, and his father, Louis, became Emperor.3 years later in 817, Arnulf, aged 23, was appointed count of Sens in Burgundy. He was the first son of Louis the Pious, but he did not inherit land because he was illegitimate. In April 841, a year after his father had died at the age of 62,he died at Sens (just before the Treaty of Verdun between his fathers legitimate surviving sons).