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# 1. 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 | ||||

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[[[]],[]] |
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There are $\operatorname{Cat}(n) = \frac{1}{n+1}\binom{2n}{n}$ ordered trees with $n+1$ nodes, see OEIS:A000108.

# 2. Additional information

**Feel free to add further combinatorial information here!**

# 3. References

# 4. Sage examples

# 5. 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.