combinatorics – Number of partitions of an integer with a fixed number of parts


Is there an easy way in Mathematica to find the number of partitions of $n$ into $k$ parts? Or equivalently, the number of partitions of $n$ with largest part equal to $k$?

I realize the function IntegerPartitions[n,{k}] will return a list of all such partitions, which I could count, but I am wondering if there is a more efficient method.