We know formulae to both
- The total number of unlabelled binary trees
- The total number of labelled binary trees
We've to figure out which one is to be applied here.
We'll need to obtain all the structurally independent binary trees, and then decide which node is A or B or C or D for that structurally independent tree — to get the given pre-order sequence.
Structurally independent $\equiv$ unlabelled binary trees.
So, 4th Catalan number.
$\frac{8*7*6*5}{5*4*3*2}=14$