Solve the Recurrence Relation T(n)=sum of T(i)T(n-i) $T(1)=1 \\
T(n) = \sum_{i=1}^{n-1}T(i)T(n-i) \\
$

I have been trying to get rid of the Summation using the T(n+1) - T(n) technique, but I can't figure out how to apply it to this. 

I used recursion trees but got too messy.

Now I'm wondering if there is an elegant solution to this recurrence.
Hint.
$$\frac{T(n+1)}{T(n)}=a(n)$$
$$a(n)-a(n-1)=b(n)$$
$$3\left(\frac{1}{b(n)}-\frac{1}{b(n-1)}\right)=c(n)$$
$$c(n)-c(n-1)=1$$
Hint.
$$\frac{T(n+1)}{T(n)}=a(n)$$
$$a(n)-a(n-1)=b(n)$$
$$3\left(\frac{1}{b(n)}-\frac{1}{b(n-1)}\right)=c(n)$$
$$c(n)-c(n-1)=1$$