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

0,5

Comments

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

Links

Table of n, a(n) for n=0..32.

John Tyler Rascoe, Python program.

Kevin Ryde, PARI/GP program

Example

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

Prog

(Python) # see links
(PARI) \\ see links

Crossrefs

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

Sequence in context: A104383 A205480 A108523 * A157003 A380054 A245900

Adjacent sequences: A382057 A382058 A382059 * A382061 A382062 A382063

Keyword

nonn

Author

John Tyler Rascoe, Mar 14 2025

Status

approved