From what I've gathered, this article details what is most likely what happened:
http://miceage.micechat.com/kevinyee/ky070609a.htm

I remember it in the 80s. It was on Nick at Nite, either just before or after The Monkees. Seriously.

Oh my God, you have no idea what this means to me. You see, I had my small part in this. My uncle did the arrangement for the piano, and he needed a copy of the song to do that, and I was the youngest one in the family, so he called me up to see if I had it lying around. I didn't, but I went to Toys R Us and bought a tape of Sesame Street songs that had it. Sigh. I'd always wanted to hear the finished product and I never did until just now. Thank you so much.