I just came across an article of almost two years ago (in Dutch: http://nos.nl/artikel/580702-willem-i-en-iii-hadden-bastaarden.html)
where it is mentioned that king William I had four extramarital children with a woman called Julie von der Goltz (Juliane Karoline Philippine von der Goltz). The first one was born in October 1807
Juliane Karoline Philippine barones von der Goltz werd geboren op 5 september 1780 als tweede dochter van Karl Franz baron von der Goltz en Henriette Wilhelmine Bärmann