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Probably mid to late 20th century story. I believe the title is something like "Farewell Ilya" or "Goodbye..."
The alien tells the story. Actually, perhaps the astronauts are the aliens, since I think it takes place on another planet. I think the narrator is injured, or somehow gets "taken in" by the ship's crew. They treat him sort of like a pet.
Anyway, the alien/narrator describes all sorts of human behavior. He ends up falling in love with human laughter. The alien is vehemently vegetarian and is disgusted when he is offered meat by the crew of the spaceship (something about not eating plant matter either unless covered under some treaty). I think he moves by folding in appendages and rolling?? Despite all the bad things he observes, he is so taken with human laughter that he leaves with the crew.
The story may be in a letter format.
I read this years ago and cannot find it in any anthologies I own nor through internet searches.