%I A061575
%S A061575 0,1,0,2,2,7,14,41,107,307,871,2546,7497,22380,67366,204517,625132,
%T A061575 1922700,5945469,18473841,57649699,180602285,567772883,1790663427,
%U A061575 5663969707,17963483548,57112388657,181994536484,581168157605
%N A061575 Number of planar planted trees with n non-root nodes and without isolated 
               2-valent nodes.
%C A061575 An isolated 2-valent node is a 2-valent node non-adjacent to any other 
               2-valent node.
%D A061575 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 
               1983,(2.7.11).
%F A061575 G.f.: Sum_{i >= 0} 1/(i+1)*binomial(2*i, i)*x^(i+1)*((1+x^3)/(1-x^2))^(i+1)*(1+x*(1+x^3)/
               (1-x^2))^(-(i+1)) or (1-x^2+x^3-sqrt((1-x^2+x^3)*(1-4*x+3*x^2-3*x^3)))/
               (2-2*x^2+2*x^3).
%Y A061575 Sequence in context: A156435 A162460 A061274 this_sequence A133602 A137249 
               A051769
%Y A061575 Adjacent sequences: A061572 A061573 A061574 this_sequence A061576 A061577 
               A061578
%K A061575 nonn
%O A061575 0,4
%A A061575 Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 13 2001