%I A052319
%S A052319 1,1,1,2,7,28,131,720,4513,31824,249513,2151744,20242983,206313024,
%T A052319 2264425179,26628836352,334022337153,4451717814528,62820790592913,
%U A052319 935750983412736,14672143677452679,241555066200437760
%N A052319 Number of increasing rooted trimmed trees with n nodes.
%C A052319 In an increasing rooted tree, nodes are numbered and numbers increase 
               as you move away from root.
%C A052319 A trimmed tree is a tree with a forbidden limb of length 2.
%C A052319 A tree with a forbidden limb of length k is a tree where the path from 
               any leaf inward hits a branching node or another leaf within k steps.
%C A052319 a(n)=number of permutations on [n+1] beginning with 12 and avoiding a 
               consecutive 132 pattern (n>=1). For example, a(4)=2 counts 12345, 
               12453. - Ralf Stephan, Apr 25 2004
%H A052319 S. Kitaev and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0205182">
               Simultaneous avoidance of generalized patterns</a>.
%H A052319 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A052319 S. Kitaev, <a href="http://www.mat.univie.ac.at/users/slc/public_html/
               wpapers/s48kitaev.html">Generalized pattern avoidance with additional 
               restrictions</a>, Sem. Lothar. Combinat. B48e (2003).
%F A052319 E.g.f.: A(x) = 1/B(-x) where B'(x) is e.g.f. of A006882 and B(0) = 1.
%F A052319 E.g.f. satisfies A'(x) = exp(A(x)-x^2/2).
%F A052319 E.g.f.: exp(-x^2/2)/(1-int[0..x, exp(-x^2/2)]). - Ralf Stephan, Apr 25 
               2004
%Y A052319 Cf. A002955, A002988-A002992, A052318-A052329.
%Y A052319 Sequence in context: A112565 A118926 A127084 this_sequence A127783 A116539 
               A141318
%Y A052319 Adjacent sequences: A052316 A052317 A052318 this_sequence A052320 A052321 
               A052322
%K A052319 nonn,eigen
%O A052319 1,4
%A A052319 Christian G. Bower (bowerc(AT)usa.net), Dec 11 1999. Formula updated 
               Mar 06, 2001.