%I A120803
%S A120803 1,1,1,2,2,4,4,8,9,16,20,37,47,80,111,183,256,413,591,940,1373,2159,
%T A120803 3214,5067,7649,12054,18488,29203,45237,71566,111658,176710,276870,
%U A120803 437820,687354,1085577,1705080,2688285,4221333,6644088,10425748
%N A120803 Number of series-reduced balanced trees with n leaves.
%C A120803 In other words, rooted trees with all leaves at the same level and no 
               node having exactly one child; the order of children is not significant.
%F A120803 Let s_0(n) = 1 if n = 1, 0 otherwise; s_{k+1}(n) = EULER(s_k)(n) - s_k(n), 
               where EULER is the Euler transform. Then a_n = sum_k s_k(n). (s_k(n) 
               is the number of such trees of height k.) Note that s_k(n) = 0 for 
               n < 2^k.
%Y A120803 Cf. A119262, A007059, A000669, A001003.
%Y A120803 Sequence in context: A016116 A060546 A163403 this_sequence A000011 A022476 
               A000013
%Y A120803 Adjacent sequences: A120800 A120801 A120802 this_sequence A120804 A120805 
               A120806
%K A120803 nonn
%O A120803 1,4
%A A120803 Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 18 2006