They took part in the 1980 contest with the song "Tænker Altid På Dig" (transl. "Always Thinking Of You"). They scored a total of 25 points ending No.14(out of 19).
This was back when each country had to sing in its native language.
By the way, Denmark didn't take part in the Eurovision Song Contest 1967 - 77 so not a bad guess really.
Unfortunately Bamse, real name Flemming Jørgensen, died in his sleep New Years Eve 2010/11. Much missed ikon of the Danish music scene.
There's not many people in Denmark who don't know this 45. Played constantly to this day by young and old alike ever since first released back in 1975. The danish text has absolutely nothing to do with "lions sleeping tonight" by the way!