A382060 Number of rooted ordered trees with n nodes such that the degree of each node is less than or equal to its depth plus one.

1, 1, 1, 1, 2, 4, 10, 27, 77, 231, 719, 2302, 7541, 25177, 85405, 293635, 1021272, 3587674, 12713796, 45402113, 163244197, 590529759, 2147915920, 7851127319, 28826079193, 106268313333, 393218951710, 1459969448090, 5437679646441, 20311366912839, 76072367645347, 285623120079865, 1074888308119285

Offset: 0

Author

John Tyler Rascoe, Mar 14 2025

Keywords

• nonn

Comments

The root vertex is depth d=0 and is to have <= d+1 = 1 children so these are "planted" trees.

Examples

			a(5) = 4 counts:
                               depth:
   o     o       o       o       0
   |     |       |       |
   o     o       o       o       1
   |     |      / \     / \
   o     o     o   o   o   o     2
   |    / \    |           |
   o   o   o   o           o     3
   |
   o                             4
		

Links

• John Tyler Rascoe, Python program.
• Kevin Ryde, PARI/GP program

Crossrefs

Cf. A000081, A000108, A000957, A036765, A288942, A358586, A358590, A380761.

Programs

PARI

\\ see links

Python

# see links