%I A093637
%S A093637 1,1,2,4,9,20,49,117,297,746,1947,5021,13378,35237,95123,254825,694987,
%T A093637 1882707,5184391,14177587,39289183,108337723,301997384,837774846,
%U A093637 2347293253,6546903307,18417850843,51617715836,145722478875
%N A093637 G.f.: A(x) = Product_{n>=0} 1/(1-a(n)*x^(n+1)) = Sum_{n>=0} a(n)*x^n.
%C A093637 Comment from David Callan, Nov 02 2006: a(n) = number of (unlabeled, 
               rooted) ordered trees on n edges such that, for each vertex of outdegree 
               >= 1, the sizes of its subtrees are weakly increasing left to right. 
               This notion is close to that of unlabeled, unordered rooted tree 
               (A000081) but, for example,
%C A093637 ./\...../\.
%C A093637 |./\.../\.|
%C A093637 |.........|
%C A093637 count as two different trees here whereas A000081 treats them as the 
               same.
%e A093637 1/((1-x)(1-x^2)(1-2x^3)(1-4x^4)(1-9x^5)...) = 1 + x + 2x^2 + 4x^3 + 9x^4 
               + ...
%o A093637 (PARI) a(n) = polcoeff(prod(i=0,n-1,1/(1-a(i)*x^(i+1)))+x*O(x^n),n)
%Y A093637 Cf. A000081, A093635, A093638.
%Y A093637 Sequence in context: A145550 A000081 A124497 this_sequence A068051 A032289 
               A006648
%Y A093637 Adjacent sequences: A093634 A093635 A093636 this_sequence A093638 A093639 
               A093640
%K A093637 nonn
%O A093637 0,3
%A A093637 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2004