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%I #6 Feb 15 2022 20:55:22
%S 1,2,5,13,35,94,255,691,1876,5092,13829,37553,101992,276995,752307,
%T 2043218,5549310,15071694,40934215,111175866,301949926,820085698,
%U 2227325273,6049340413,16429805791,44622800991,121194031561,329158925122,893984605415,2428032213452
%N 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 If the condition "d divides w" in the definition is replaced by "d<=w" then sequence A000108 (the Catalan numbers) is obtained.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a054/A054657.java">Java program</a> (github)
%K nonn
%O 1,2
%A _John W. Layman_, Apr 17 2000
%E More terms from _Sean A. Irvine_, Feb 15 2022
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