There are 23 statistics on Ordered trees in the database:
(and possibly some waiting for verification)

St000084Ordered trees ⟶ ℤ
The number of subtrees.
St000085Ordered trees ⟶ ℤ
The number of linear extensions of the tree.
St000094Ordered trees ⟶ ℤ
The depth of an ordered tree.
St000166Ordered trees ⟶ ℤ
The depth minus 1 of an ordered tree.
St000167Ordered trees ⟶ ℤ
The number of leaves of an ordered tree.
St000168Ordered trees ⟶ ℤ
The number of internal nodes of an ordered tree.
St000328Ordered trees ⟶ ℤ
The maximum number of child nodes in a tree.
St000397Ordered trees ⟶ ℤ
The Strahler number of a rooted tree.
St000400Ordered trees ⟶ ℤ
The path length of an ordered tree.
St000410Ordered trees ⟶ ℤ
The tree factorial of an ordered tree.
St000413Ordered trees ⟶ ℤ
The number of ordered trees with the same underlying unordered tree.
St000415Ordered trees ⟶ ℤ
The size of the automorphism group of the rooted tree underlying the ordered tree.
St000416Ordered trees ⟶ ℤ
The number of inequivalent increasing trees of an ordered tree.
St000417Ordered trees ⟶ ℤ
The size of the automorphism group of the ordered tree.
St000521Ordered trees ⟶ ℤ
The number of distinct subtrees of an ordered tree.
St000522Ordered trees ⟶ ℤ
The number of 1-protected nodes of a rooted tree.
St000523Ordered trees ⟶ ℤ
The number of 2-protected nodes of a rooted tree.
St000679Ordered trees ⟶ ℤ
The pruning number of an ordered tree.
St000700Ordered trees ⟶ ℤ
The protection number of an ordered tree.
St000973Ordered trees ⟶ ℤ
The length of the boundary of an ordered tree.
St000974Ordered trees ⟶ ℤ
The length of the trunk of an ordered tree.
St000975Ordered trees ⟶ ℤ
The length of the boundary minus the length of the trunk of an ordered tree.
St001058Ordered trees ⟶ ℤ
The breadth of the ordered tree.