A recurrence relation similar to Catalan number

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Consider the convolutional recurrence relation below: $$T(n)=\begin{cases}\displaystyle\sum_{k=1}^{n−1} k\cdot T(k)\cdot T(n−k) & n\ge2\\ 1 &n=1 \end{cases}$$

Does it have a closed form? Or is it possible to get a tight upper bound of $T(n)$?