It is the Bobby Troupe "Route 66". Arrangement and orchestra conducted by Nelson Riddle -- who was pretty good at what he did, too. Frank, for example, would know...
From Wikipedia:
Nelson Riddle was commissioned to write the instrumental theme when CBS decided to have a new song, rather than pay royalties for the Bobby Troup song “(Get Your Kicks on) Route 66.” Riddle’s theme, however, offers an unmistakable homage to the latter’s piano solo (as originally recorded by Nat King Cole) throughout the number.