Here are two of the three most influential jazz trumpeters ever: Dizzy Gillespie and Louis Armstrong.
I don't know who the pianist and others are, what the year is (certainly post-1953 since Dizzy's trumpet is bent) and whether these two made any other recordings together. But this pairing is particularly interesting since Dizzy, with Charlie Parker, was the founder of bebop, and Louis never embraced that style of jazz, with its "weird" chords and complicated melodies and rhythms. By 1953, however, the debate was over: bebop was mainstream jazz and Louis had become more a popular entertainer than a cutting-edge jazz musician. This song is popular entertainment, and good fun.
The third great jazz trumpeter was, of course, Miles Davis. Miles played with Dizzy in his early days, but I don't know whether he ever played with Louis.