Q: I would very much appreciate you telling me what this is. The picture includes the leaves, the nut case and the nut. I found a total of 8-10 bushes with nuts on them. I think it may be a type of Hickory but I am not sure.
A: You found a bottlebrush buckeye. This large shrub is gorgeous in spring when it produces many huge spikes of white flowers. Swallowtail butterflies love them.
The flowers are followed by one or more seed pods, which you first noticed.
If you want to plant the seed, do it as soon as you find them, in a sunny bed. They will likely sprout next spring.