My suggestion would be to post a picture of the "nuts" and the leaves (whole leaves may be made up of many leaflets) of the tree. The better the pictures, the better chance we can ID the tree. If the nuts will peel, you might also want to see what's underneath the skin.

Probably 'aborted' walnutlets that weren't adequately pollenated or otherwise not properly developing. It's a common phenomenon.
Agree, photos would be more likely to allow us to give a defintive dx.

Thanks so much for the replies. I believe this is a very mature walnut tree because the lower branches are very high up and the leaves look identical to a walnut. I was not famiiar with "aborted" ones but I would bet that is what these are. After opening, I would find walnut meat inside. Funny how this seems to happen most years at this time.