Don’t forget Carter, also.
I think there are too many ex-Presidents, with all their security details. Not inviting any of them isn’t a slight, it’s probably a matter of practicality.
I’m also not sure that the White House actually knows who was and wasn’t invited. An invitation to something doesn’t usually come with a guest list.
Of course we all know the White House would never, ever lie! /sarc
We also know they can be incredibly petty.