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This is part of the TV Show Astaire Time (last one) from 25 September 1960.
Astaire suggested to Count: “You just play and I’ll dance,” And Basie replied “No, no. You dance and I’ll play.”

“Sweet Georgia Brown” was the performed song and the others members of the Count Basie Orchestra on this video:
Joe Newman, Snooky Young, Thad Jones , Sonny Cohn – trumpet
Henry Coker, Benny Powell, Al Gray – trombone
Marshall Royal, Frank Foster, Frank Wess, Billy Mitchell , Charlie Fowlkes – reeds
Freddie Green – guitar
Eddie Jones – bass
Sonny Payne – drums