Can this recursive summation function be simplified?

Question

I have the recursive function

$$ a_n = \sum_{x=1}^n a_{n-x} a_{x-1} $$

where $a_0=1$ and $n$ is a positive integer. Looking at a graph of this function, it's very exponential in form, but it's not perfectly exponential.. I'm not very educated on summations or recursive functions.

Can this function be simplified in any way?

Answer 1

See Catalan Numbers, which are closely related to your expression.

Answer 2

Catalan numbers. See OEIS sequence A000108