%I A054657
%S A054657 1,2,5,13,35,94,255,691,1876,5092,13829
%N A054657 Number of leaves on the rooted tree of height n constructed by the following 
               rule. Assign weight 1 to the single node at height 1. At each node 
               of weight w at height k>0, branch to nodes at height k+1 as follows: 
               one node of weight 1 and a node of weight d+1 if d divides w.
%C A054657 If the condition "d divides w" in the definition is replaced by "d<=w" 
               then sequence A000108 (the Catalan numbers) is obtained.
%Y A054657 Sequence in context: A048781 A097919 A160438 this_sequence A024576 A057960 
               A007075
%Y A054657 Adjacent sequences: A054654 A054655 A054656 this_sequence A054658 A054659 
               A054660
%K A054657 nonn
%O A054657 1,2
%A A054657 John W. Layman (layman(AT)math.vt.edu), Apr 17 2000