Number of prime knots with n crossings
Mathematica + KnotTheory`, 13 bytes
NumberOfKnots

I didn't know this built-in function existed when I commented that the package might be useful. Everyone else had an equal chance to find it, since I commented about the library. I found it in the list of Lightly Documented Features. Still, I won't accept this answer, since I want to see answers by other people.