We have a split entry that is minuscule with stairs heading either up or down and a tiny landing. I would like to remove the wall separating the up from the downstairs (it may be the only wall that the stairs are attached to as one side of the stairway is a brick wall) and make the entry look a fraction bigger. How can I know if this is safe to do? 

If not, can I remove the upper drywall and add molding to the studs to create a visually more open space? Would the studs be too large to be appealing? We have been remodeling our home for the last couple of years but the entry has me stumped. Don't want to weaken the house structure but it looks bad.

The house was built in 1968 so it is 48 years old.