[SeqFan] Number of linear extensions of divisibility lattices and of other posets?

[Christian G.Bower]

For this concept on rooted trees and general posets, consider the concept
of an increasing rooted tree.  This is a rooted tree whose nodes are
numbered 0 to n-1 such that the root is numbered 0 and any child of a
node is numbered greater than its parent.  Several examples can be found
in the EIS (mostly authored by myself) by doing a word search of
"increasing rooted."  The most fundamental examples can't be found that
way because they correspond to sequences better known for other reasons.

Increasing rooted trees are given by (n-1)! See A000142.

Increasing ordered rooted trees: (2n-3)!! See A001147.

Increasing binary rooted trees: a(2n-1) = A002105(n).

Increasing ordered binary rooted trees: a(2n-1) = A000182(n)
tangent numbers.

Increasing posets: A006455.

Christian