"April in Paris" is a song composed by Vernon Duke with lyrics by E. Y. Harburg in 1932 for the Broadway musical, Walk a Little Faster. Count Basie's 1955 recording (recorded July 26, 1955 at Fine Sound, New York City) is the most famous, and that particular performance was inducted into the Grammy Hall of Fame. On this recording, trumpeter Thad Jones played his famous "Pop Goes the Weasel" solo, and Basie directs the band to play the end "one more time," then "one more once."
Frank Sinatra was a big fan of Count Basie, and often referenced him in song ("Hey there cutes, put on your Basie boots" from "Come Dance with Me") and otherwise. The ending of the title track to Nice 'n' Easy (1960) references the "April in Paris" recording with the singer's seemingly off the cuff "Like the Man says, 'One more time.'"
This site provides some additional details about the '55 Basie recording:
The opening classic title track (to April in Paris) was arranged by organist Wild Bill Davis, a forgotten master of the instrument who certainly belongs up there with Jimmy Smith and Jack McDuff. It became Basie's biggest hit, charging up to number 28 on the pop charts. The arrangement is expansive and features the classic Basie reed section that is smooth as can be without becoming syrupy. Thad Jones lays in with a nice trumpet solo and we also get a solo from Benny Powell, who obtains the sweetest sound I've ever heard from a trombone. Then there's the matter of Basie's repeated "one more time" false endings, which certainly must have added to the record's popularity with the general public. In any case, when it is over, it's pretty hard not to just start the song up all over again.
Sounding a little bit like the classic "Miller sound" of Glenn Miller and Orchestra, when that "classic Basie reed section that is smooth as can be without becoming syrupy" kicks in after the trumpet solo (the "Pop goes the weasel" solo on the 1955 recording, located at 1:45 in the following video of a live performance), I think it has to be considered one of the most gloriously beautiful moments ever captured in the history of recorded music. Here Basie and band performs "April In Paris," "Big Brother," and "Jumpin' At The Woodside" for a surprisingly mixed race crowd in what appears to be the late fifties, so you want to watch at least the first song: