Question: Which noble dynasty of Austrian margraves and dukes was Henry I a member of? 

Context paragraphs:
Eduard Taaffe, 11th Viscount Taaffe: Eduard Franz Joseph Graf von Taaffe, 11th Viscount Taaffe (24 February 1833 – 29 November 1895) was an Austrian statesman, who served for two terms as Minister-President of Cisleithania, leading cabinets from 1868 to 1870 and 1879 to 1893.  He was a scion of the Irish Taaffe noble dynasty, who held hereditary titles from two different countries: Imperial Counts ("Reichsgrafen") of the Holy Roman Empire and viscounts in the Peerage of Ireland (in the United Kingdom).

Counts of Celje: The Counts of Celje (Slovene: "Celjski grofje" ) or the Counts of Cilli (German: "Grafen von Cilli" ; Hungarian: "cillei grófok" ) were the most influential late medieval noble dynasty on the territory of present-day Slovenia.  Risen as vassals of the Habsburg dukes of Styria, they ruled the County of Cilli as immediate counts ("Reichsgrafen") from 1341 and rose to Princes of the Holy Roman Empire in 1436.  However, the line became extinct when the last count Ulrich II of Celje was killed in 1456.

Elder House of Welf: The Elder House of Welf was a Frankish noble dynasty of European rulers documented since the 9th century.  Closely related to the Carolingian dynasty, it consisted of a Burgundian and a Swabian group.  It has not been definitively clarified, however, whether the two groups formed one dynasty or whether they shared the same name by coincidence only.  While the Elder House became extinct in the male line with the death of Duke Welf of Carinthia in 1055, his sister Kunigunde married into the Italian House of Este and became the ancestor of the (Younger) House of Welf.

Windisch-Graetz: The House of Windisch-Graetz, also spelled Windisch-Grätz, is an Austrian aristocratic family, descending from Windischgraz in Lower Styria (present-day Slovenj Gradec, Slovenia).  The noble dynasty serving the House of Habsburg achieved the rank of "Freiherren" in 1551, of Imperial Counts in 1682 and of Princes of the Holy Roman Empire in 1804.

Henry I, Margrave of Austria: Henry I (German: "Heinrich" , died 23 June 1018), known as Henry the Strong (German: "Heinrich der Starke" ), was the Margrave of Austria from 994 to his death in 1018.  He was a member of the House of Babenberg.

Margraviate of Austria: The Margraviate of Austria was a southeastern frontier march of the Holy Roman Empire created in 976 out of the territory on the border with the Kingdom of Hungary.  Originally under the overlordship of the Dukes of Bavaria, it was ruled by margraves of the Franconian Babenberg dynasty.  It became an Imperial State in its own right, when the Babenbergs were elevated to Dukes of Austria in 1156.

Maximilian Karl Lamoral O'Donnell: Maximilian Karl Lamoral Graf O’Donnell von Tyrconnell (October 29, 1812 — July 14, 1895) was an Austrian officer and civil servant who became famous when he helped save the life of Emperor Franz Josef I of Austria.  O'Donnell was a descendant of the Irish noble dynasty of O'Donnell of Tyrconnell.

House of Babenberg: The House of Babenberg was a noble dynasty of Austrian margraves and dukes.  Originally from Bamberg in the Duchy of Franconia (present-day Bavaria), the Babenbergs ruled the Imperial Margraviate of Austria from its creation in 976 AD until its elevation to a duchy, and from then until the extinction of the line in 1246, whereafter they were succeeded by the House of Habsburg.

Terter dynasty: Terter (Bulgarian: Тертер ), also Terterids or Terterovtsi (Тертеровци), was a Bulgarian noble and royal house of Cuman origin, a branch of the Cuman noble dynasty of Terteroba, that ruled the Second Bulgarian Empire between 1280 and 1292, as well as between 1300 and 1323.

Koli Tenguella: Koli Tenguella (or Koli Tengella Jaaje Baa alias Koli Pullo) (1512–1537) was a Fulani warrior.  In the sixteenth century , after nine attempts, he conquered Futa Toro, a kingdom located in the northeast of the current Senegal and founded the new dynasty Fulani Denianke.  He is the ancestor of the royal and noble dynasty Déniyankobés, the Bâ genealogy to which also belong to the Koli clans Teghéla, Rella, Dianga, Soulé, diye, Waranka, but also those of Sanghé Lobaly, Waly and Sinthiane Padalal.

Supporting paragraphs: Henry I, Margrave of Austria House of Babenberg
Answer: The House of Babenberg