%I A007863
%S A007863 1,2,7,31,154,820,4575,26398,156233,943174,5785416,35955297,
%T A007863 225914342,1432705496,9158708775,58954911423,381806076426,
%U A007863 2485972170888,16263884777805,106858957537838
%N A007863 Number of hybrid binary trees with n nodes.
%D A007863 N. S. S. Gu, N. Y. Li and T. Mansour, 2-Binary trees: bijections and 
               related issues, Discr. Math., 308 (2008), 1209-1221.
%D A007863 J.M. Pallo, On the listing and random generation of hybrid binary trees, 
               International Journal of Computer Mathematics, 50, 1994, 135-145.
%H A007863 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A007863 G.f. satisfies x^2*A(x)^3+x*A(x)^2+(-1+x)*A(x)+1 = 0.
%F A007863 a(n) = 3F2({-n, n+1, n+2 } ; {1, 3/2})( -(1/4) ) [From Olivier GERARD 
               (olivier.gerard(AT)gmail.com), Apr 23 2009]
%p A007863 A:= proc(n) option remember; if n=0 then 1 else convert (series ((x^2*A(n-1)^3 
               +x*A(n-1)^2 +1)/ (1-x), x=0,n+1), polynom) fi end: a:= n-> coeff 
               (A(n), x,n): seq (a(n), n=0..19); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 22 2008]
%t A007863 InverseSeries[Series[(y-y^2-y^3)/(1+y), {y, 0, 24}], x] (* then A(x)=y(x)/
               x *) - Len Smiley Apr 14 2000
%t A007863 Table[ HypergeometricPFQ[{-n, 1 + n, 2 + n}, {1, 3/2}, -(1/4)], {n,0,
               20}] [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]
%o A007863 (Macsyma) taylor_solve_choose_order:true; taylor_solve( A^3*X^2+A^2*X+A*(X-1)+1,
               A,X,0,[ 20 ]);
%Y A007863 Cf. A007788.
%Y A007863 Sequence in context: A076177 A007164 A126033 this_sequence A030823 A030873 
               A030913
%Y A007863 Adjacent sequences: A007860 A007861 A007862 this_sequence A007864 A007865 
               A007866
%K A007863 nonn
%O A007863 0,2
%A A007863 pallo(AT)u-bourgogne.fr (Jean Pallo)