A #1 hit for Frank in 1955, it must have been a great jukebox song. You can find it on the Capitol Singles Collection or just get the individual track here.
Frank swings it again later with Basie but I prefer this Nelson Riddle arrangement.
I'm updating to add a link to Mark Steyn's definitive piece on this great song and its surprisingly controversial history. Here's Mark on the two versions:
It's an up song about feeling down, with four terrific trumpeters - Harry "Sweets" Edison, Conrad Gozzo, Manny Klein, and Mickey Mangano - blowing very cool, and Frank Flynn, the guy who wallops that monster gong on "Road To Mandalay", taking over on vibes for the last part of the first chorus. And it was a big hit: Number Two in Britain, Number Two on the Cashbox charts, Number Two on the Billboard bestsellers chart, and Number One on Billboard's airplay chart, where on July 16th it got knocked off by "Rock Around The Clock" and then came roaring back and toppled Bill Haley from the top spot on July 23rd. That's to say, it held its own with a record that wasn't merely a hit but came to embody the triumph of a new and dominant form that would crush the music Sinatra loved. "Learnin' The Blues" isn't rock'n'roll, but it has an insistence and energy that matches anything Haley's Comets can offer. Ben Barton was so impressed he gave Stanley Cooper a $100 bonus.Yup.
Frank liked "Learnin' The Blues" and seven years later he remade it on his first LP with Count Basie. This is one of the great vocal albums in the entire history of recorded music, and Neal Hefti's arrangements are spectacular - on "I Won't Dance", "Pennies From Heaven", "I Only Have Eyes For You"... But, along with the remake of "Tender Trap", "Learnin' The Blues" is a very slight disappointment. It's one of the longer tracks on the set - four-and-a-half minutes - and it shows off the band nicely, but almost immediately settles into an easy Basie groove with a characteristically Hefti back-and-forth between the muted trumpets and the saxes. Where Riddle's version is restless and driven, Hefti's chart sounds a long way away from the sleepless nights and cigarettes and all the other imagery. "Learnin' The Blues" is what it is: a rough-and-ready pop song, and in smoothing out a lot of those rough edges something gets lost along the way.
Bonus: this wonderful version by Ella and Louis: