A246565 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly increasing.

1, 1, 2, 3, 6, 9, 20, 31, 67, 115, 238, 406, 880, 1494, 3118, 5568, 11408, 20092, 41938, 73687, 151529, 272359, 552611, 987277, 2033173, 3617167, 7371745, 13318869, 26991289, 48496985, 99264686, 177917588, 362349258, 655925568, 1331038563, 2401097768, 4913906801, 8844673793, 18046697901, 32720071992, 66666578597

Offset: 0

Author

Joerg Arndt, Aug 30 2014

Keywords

• nonn

Examples

			The a(4) = 6 such trees are:
:
:   1:
:  [ 1 1 1 1 ]
:  [ 0 0 0 0 ]
:
:  O--o
:  .--o
:  .--o
:  .--o
:
:
:   2:
:  [ 1 1 2 ]
:  [ 0 0 0 ]
:
:  O--o
:  .--o
:  .--o--o
:
:
:   3:
:  [ 1 3 ]
:  [ 0 0 ]
:
:  O--o
:  .--o--o--o
:
:
:   4:
:  [ 2 2 ]
:  [ 0 0 ]
:
:  O--o--o
:  .--o--o
:
:
:   5:
:  [ 2 2 ]
:  [ 0 1 ]
:
:  O--o--o
:     .--o--o
:
:
:   6:
:  [ 4 ]
:  [ 0 ]
:
:  O--o--o--o--o
:
See the Arndt link for all trees for 0 <= n <= 7.
		

Links

• Joerg Arndt, All trees for 0 <= n <= 7

Crossrefs

Cf. A000108 (all trees), A246566 (descending branch lengths), A193196, A192243.