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%I #9 Jul 08 2014 12:39:31
%S 1,1,2,4,10,25,68,187,530,1523,4447,13121,39107,117490,355507,1082234,
%T 3312255,10185125,31450633,97480337,303157086,945671951,2958113722,
%U 9276528602,29158191215,91845796986,289874628176,916536727561
%N Number of ordered rooted trees on n nodes with thinning limbs.
%C A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.
%H Alois P. Heinz, <a href="/A124344/b124344.txt">Table of n, a(n) for n = 1..150</a>
%F G.f.: A(x) = A0(x)+A1(x)+A2(x)+... where A0(x)=x, An(x) = x*(A0(x)+A1(x)+...+An(x))^n.
%Y Cf. A000108, A124343-A124348.
%Y Row sums of A124328.
%K nonn
%O 1,3
%A _Christian G. Bower_, Oct 30 2006, suggested by _Franklin T. Adams-Watters_