If it is a close friend he would have asked you to be apart of his groomsmen... or whatever they are called, but nooooooooo Not a good friend.
You are badly in need of wisdom to get you happy in your mind. Think of these words in your life: longevity, health, love, peace, money, family, forgiveness, kind, benevolence....etc. now just say to yourself that you don't need an invitation to a wedding to achieve all those things! Having had this treatment and is effective, now listen to you wife and send a present ... it will give happiness, love, forgiveness, kindness... to the wedding couple (unless they are materialistic but such a fleeting memory may last in one's conscience). Remember you may never know why you are not invited, there is a hundred and one reasons as to why you are not, people's action may not be malicious or intentional as they may be victim of their circumstance. However if your conscience is clear , give before you take makes the world more peaceful.
I think in consideration, you guys haven't met in a while, just let bygones be bygones. Did you invite him to your wedding? If it's a small reception then it makes sense that he didn't invite you.