Should I?

My sons father has been in and out of his life the whole two years he's been on this earth. He now hasn't seen our child in four months and hasn't contacted me in any way in weeks and honestly it doesn't look like he plans to any time soon. I used to send him pictures of our son and keep him updated when he was a tiny bit involved but I was wondering if I should still do that or not? I personally don't want to because I feel like if he wants to see his son or cared about how he is he would contact me buuuut he's also the type of person that runs around telling people I keep our son from him and all kinds of crap basically a giant sob story to make himself feel better about the fact that he doesn't come around. Ever since he got a new gf and had another baby that's when he just completely stopped coming around. It was like he got a new family and ditched our child. Anyways should I keep him updated or not? I just don't want people to believe him and thinking that I'm keeping our son from him and not letting him know anything about our son when it's absolutely not true.