Airborne divisions were counted as light infantry divisions and thus numbered in order as part of the infantry divisions. The other light infantry specialized division, the 10th mountain division, was also included in the regular infantry ordering. Part of the reason for this was that most of the airborne divisions had existed before WWII. Upon reactivation, certain divisions were marked as airborne and trained as such. So they weren't new formations, they had history before converting to airborne.

These divisions existed as regular infantry formations during World War I, and simply changed roles while retaining their numbers during WWII; the 82nd and 101st Infantry Divisions were raised from draftees as part of the National Army and fought in World War I. They were then deactivated after the war and placed in the Organized Reserves, only existing "on paper". The patches of the divisions in World War I were pretty much the same as they were in WWII, just without the small "AIRBORNE" tab. The 82nd Infantry Division was reactivated in March 1942 and converted into the United States' first airborne division in August; the 101st Airborne did the same, and hence was the second.

The odd "gap" in infantry divisions from 11-23 that was mostly filled by the armored divisions in WWII, did actually consist of infantry divisions at one point; most of these infantry divisions were formed too late to see service in World War I, and hence have little to no history because they were deactivated before even going overseas.

Sources:

http://www.history.army.mil/html/forcestruc/cbtchron/cc/082abd.htm

http://www.history.army.mil/html/forcestruc/cbtchron/cc/101abd.htm