# Is “super-exponential” a precise definition of algorithmic complexity?

I cannot seem to find a precise definition of what “super-exponential” is supposed to refer to when one’s talking about an algorithm’s time complexity.

For instance, if an algorithm runs for $$nC(n-1)$$ steps, where $$C(cdot)$$ is the Catalan number, is this algorithm super-exponential in $$n$$?