Well, then you, unfortunately, only have two options if he doesn't bring it up:
1. Wait to see if it will pass on it's own; if it does, then he'll be fine. But if it doesn't and becomes lodged in his intestines, then you're looking at surgery to remove it. Dogs with corn cob obstructions can be fairly serious since many of them don't show the "classic" signs of a foreign body such as vomiting, lethargy, disinterest in food or abdominal pain. As a result, that cob can do some significant damage to the intestines when it causes an obstruction.
If the corn cob remains in the stomach for a while (which it can do), then this is a waiting game with constant monitoring of his stools for the cob and/or for signs of obstruction. It might take 12-24 hours or could take days.
2. Surgical intervention now to remove it or possibly endoscopy if your vet (or an ER clinic) has this equipment. It's not exactly the critical sort of situation where the cob needs to come out immediately in terms of toxicity, but it would be best to retrieve it while it's in the stomach, rather than once it's in the intestines (especially if an endoscope will be used to remove it).
Unfortuantely, I'm going to have to step away from my computer to help a neighbor who has health issues. I'm sorry for the inconvenience but hope you'll keep me posted about whether or not you were successful in retrieving the corn cob. I should log back on my computer in another hour or so.