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A246566 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly decreasing.

%I A246566 #7 Aug 31 2014 02:00:36
%S A246566 1,1,2,4,10,24,62,155,396,992,2504,6228,15512,38220,94059,229498,
%T A246566 558642,1350384,3255138,7801327,18642118,44329833,105111283,248184255,
%U A246566 584396849,1371048495,3208318247,7483522231,17413665881,40405120865,93543352492
%N A246566 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly decreasing.
%H A246566 Joerg Arndt, <a href="/A246566/a246566.txt">All trees for 0 <= n <= 5</a>
%e A246566 The a(3) = 4 such trees are:
%e A246566 :
%e A246566 :     1:
%e A246566 :    [ 1 1 1 ]
%e A246566 :    [ 0 0 0 ]
%e A246566 :
%e A246566 :  O--o
%e A246566 :  .--o
%e A246566 :  .--o
%e A246566 :
%e A246566 :
%e A246566 :     2:
%e A246566 :    [ 2 1 ]
%e A246566 :    [ 0 0 ]
%e A246566 :
%e A246566 :  O--o--o
%e A246566 :  .--o
%e A246566 :
%e A246566 :
%e A246566 :     3:
%e A246566 :    [ 2 1 ]
%e A246566 :    [ 0 1 ]
%e A246566 :
%e A246566 :  O--o--o
%e A246566 :     .--o
%e A246566 :
%e A246566 :
%e A246566 :     4:
%e A246566 :    [ 3 ]
%e A246566 :    [ 0 ]
%e A246566 :
%e A246566 :  O--o--o--o
%e A246566 :
%e A246566 See the Arndt link for all trees for 0 <= n <= 5.
%Y A246566 Cf. A000108 (all trees), A246565 (ascending branch lengths), A193196, A192243, A001519.
%K A246566 nonn
%O A246566 0,3
%A A246566 _Joerg Arndt_, Aug 30 2014