%I #13 Dec 12 2016 09:36:43
%S 1,1,1,1,2,3,6,11,23,47,103,223,503,1132,2602,5986,13922,32433,75994,
%T 178354,419945,990134,2339033,5531459
%N Number of trees with n unlabeled nodes such that all nodes with degree >2 lie on a single path with length equal to the tree's diameter.
%C First differs from A000055 at a(10).
%C First differs from A130131 at a(10), n >= 1.
%C The ratio of consecutive terms seems to tend to some limit. - _Andrey Zabolotskiy_, Dec 12 2016
%H Andrey Zabolotskiy, <a href="/A277795/a277795.py.txt">Python script for the sequence</a>
%e From _Andrey Zabolotskiy_, Nov 21 2016: (Start)
%e Three trees that are counted in A000055(10) but not in a(10):
%e (1)
%e o o-o-o
%e | |
%e o----o
%e | |
%e o o-o-o
%e (2)
%e o-o-o
%e |
%e o-o-o-o
%e |
%e o-o-o
%e (3)
%e o-o-o-o-o-o-o
%e |
%e o-o-o
%e (End)
%Y Cf. A000055, A130131.
%K nonn,more
%O 0,5
%A _Gabriel Burns_, Oct 31 2016
%E Corrections and more terms from _Andrey Zabolotskiy_, Nov 21 2016