What's the song Lt. Columbo wants to learn at the end of the episode ? Thanks

It's "This Old Man" - the de facto 'theme' song for the character. Like much of the rest of this episode, it's a difficult scene to watch, as it's clear he knows this song quite well (evidenced by Columbo whistling it in several episodes and actually playing a few notes of it on the piano in 'Try and Catch Me"). I suppose it's meant to show the compassionate side of his character.