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Definition & Example

An ordered tree is a rooted tree where the children of each node are ordered.

Equivalently, an ordered tree is recursively defined to be either a leaf (external node) or an ordered list of ordered trees (internal node).
the 5 Ordered trees of size 4  
[[],[],[]]  [[],[[]]]  [[[]],[]]  [[[],[]]]  [[[[]]]] 
 There are $\operatorname{Cat}(n) = \frac{1}{n+1}\binom{2n}{n}$ ordered trees with $n+1$ nodes, see OEIS:A000108.
Additional information
Feel free to add further combinatorial information here!
References
Sage examples
Technical information for database usage
 An ordered tree is uniquely represented as an empty list (leaf) or as a sorted list of ordered trees (internal node).
 Ordered trees are graded by its number of nodes.
 The database contains all ordered trees of size at most 9.
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