%I A032035
%S A032035 1,1,1,3,13,77,573,5143,54025,650121,8817001,133049339,2210979381,
%T A032035 40118485237,789221836741,16730904387183,380227386482641,
%U A032035 9221550336940241,237724953543108753,6491255423787076915
%N A032035 Number of increasing rooted 2,3 cacti (triangular cacti with bridges) 
               with n-1 nodes.
%C A032035 Also increasing involution rooted trees with n-1 nodes.
%H A032035 C. G. Bower, <a href="transforms2.html">Transforms (2)</a>
%H A032035 <a href="Sindx_Ca.html#cacti">Index entries for sequences related to 
               cacti</a>
%H A032035 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A032035 E.g.f. of a(n+1) satisfies A'(x) = exp(A(x)+A(x)^2/2)
%F A032035 E.g.f. satisfies A''(x) = 1/(1-A(x)).
%F A032035 Shifts left 2 places under "AIJ" (ordered, indistinct, labeled) transform.
%p A032035 A:= proc(n) option remember; if n=0 then x else convert (series (Int 
               (exp (A(n-1)+ A(n-1)^2/2), x), x=0, n+1), polynom) fi end; a:= n-> 
               if n=1 then 1 else coeff (A(n-1), x, n-1)*(n-1)! fi: seq (a(n), n=1..20); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
%Y A032035 Cf. A001147, A091481.
%Y A032035 Sequence in context: A059040 A074530 A159662 this_sequence A127127 A043301 
               A141762
%Y A032035 Adjacent sequences: A032032 A032033 A032034 this_sequence A032036 A032037 
               A032038
%K A032035 nonn,eigen
%O A032035 1,4
%A A032035 Christian G. Bower (bowerc(AT)usa.net), Apr 01, 1998