Hasn’t offered to buy baby anything

I cut my bd off early in my pregnancy for my peace of sanity. This whole time he has been out fucking different bitches each week and denying my baby, even went as far to tell one of the girls I confronted (asked nicely if something was going on between them because I was pregnant and he was lying to me etc.) that my child wasn’t his. Right after that she decided to publicly post videos and photos with him. She had zero compassion for me as a woman but that was my answer.

Fast forward, I give birth next month and have been buying a lot of things for the arrival of my baby. He came around half a month ago begging to let me let him be there for his daughter during the last months of pregnancy. He said the regular bullshit, wanting to be an involved father, be there for all the upcoming appointments etc. I decided to give him the benefit of the doubt and give him the chance to be an active father. My issue is he hasn’t offered to buy a single thing for the baby!! And as some of you know, baby items are expensive. Luckily I have enough to support my child on my own…but just because I can doesn’t mean I should.. I feel embarrassed to even ask and say “why haven’t you offered to help out?” I don’t mind doing it all on my own, but what’s the point of begging to be a part of it when he doesn’t want to help out? I don’t feel I should even be asking, it’s common sense. He won a big settlement and has been wasting all his money on his friends, the bar, and his bitches, but not a single thing for my child? My mom said I should talk to him about it since it’s his responsibility, but my pride doesn’t let me. I don’t mind doing it in my own but I don’t like that he comes around and acts like he cares when he doesn’t. What do you recommend I do? Should I just continue to do it in my own like I have been doing it this whole time?