I think it really depends on how you count everything.
Penn State University has about 41,000 students enrolled at the Main Campus.
The University has branch campuses, spread throughout the state, where a lot of students do the first 2 years of a four year degree.
If you include the Penn State University system, there are more than 80,000 students.
And I don't think this is the largest university in the US. Don't know which one is though.
ttn1