Ex doesn't want to help with birthday party

Hi everyone, I'm looking to get some unbiased opinions on this situation.

My son is turning 5 a few short weeks and myself and his father have been separated since he was a baby. Every year for his birthday I have footed the bill to have a birthday celebration that both his side of the family and mine have attended. However this year, my son has expressed to me that he would like to have a party with his school friends. Totally reasonable In my opinion as he's getting older.

I have asked his father if he would be willing to split the bill to have a birthday party that our son wants this year with his friends and he just isn't having it. My exes girlfriend even went out of the way to tell me that she thinks that he doesn't need a party with his friends. This made me very angry, especially because this women has only been around for 3 months. The more I think about this whole situation the more angry I get. His father makes $65000 a year and can't afford $100? Sickens me.

Luckily I have amazing family that has decided that they will pay half of the cost to have the birthday my son wants.

So what I'm wondering is, would it be awful of me to not invite my ex and his girlfriend? The way I see it is that it will be a free photo op for them and my son that I care for 100% of the time.

EDIT: he does pay court ordered child support that is taken directly off his paycheques and visits once a month for the weekend, but does not take him over night by choice.

I have court ordered full custody so I will be having the party no matter what he or the gf think but because he had no other children and makes so much more then me it's very upsetting that he doesn't want to help or even be more involved.