I think you get the prize for correct ID.The leaves resemble shag bark hickory. I have several in my woods. Although the bark is somewhat similar to my oldest tree, it is nowhere near that size/age. The shag bark has large single-lobed leaves, much larger than a pig nut or regular hickory. The nuts are smaller than either the regular or pig nut, only about an inch or so in diameter with the husk on. If you also see some small, husk segments, that would be my guess, although finding them after the squirrels got to them maybe a problem.