Not actually a series -- but, rather the same kind of situation. I received fervent recommendations of the "Hoka" short stories by Poul Anderson and Gordon Dickson (wonder whether that last name is going to morph into something grotesque?) -- the recommenders found them side-splittingly funny.
The premise is that the Hoka are an alien race, teddy-bear-like in appearance, who live on a planet hugely far away. They are benign and lovable creatures; but their most prominent trait is that they are compulsive and brilliant mimickers, imitators and enactors. As soon as spacefaring humans arrive on their planet, the Hoka become fascinated by all aspects of human culture, and start imitating and re-enacting for all they're worth.
Would seem a promising idea; but I found that it wasn't really enough to support a whole string of stories -- for me, it rapidly came to seem a single, exhaustingly repetitive and monotonous joke: the Hoka kept homing in on something out of human art and culture, and very accurately imitating and re-living it -- grand opera, Tolkien, Kipling's ballads of Empire, etc. etc. Otherwise, IMO not very much point to the stories.
The one Hoka story which I really did find funny, was the very first in the series: when human / Hoka contact was very new -- the first humans to meet the Hoka were big fans of Wild West films and novels, and the Hoka immediately went overboard for all the Western stuff; but because everything was so new to them, they got a lot of Wild West features, hilariously wrong. But they were such clever imitators that very soon, they were getting everything dead right -- and for me, that seemed the sole-and-only source of humour in the situation, and I didn't find it very humorous. And the authors' one full-length Hoka novel, "Star Prince Charlie" -- that I found quite embarrassingly weak and lame, and I gather that a lot of otherwise Hoka fans would concur with that view.