0,2

N. S. S. Gu, N. Y. Li and T. Mansour, 2-Binary trees: bijections and related issues, Discr. Math., 308 (2008), 1209-1221.

J.M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50, 1994, 135-145.

Index entries for sequences related to rooted trees

G.f. satisfies x^2*A(x)^3+x*A(x)^2+(-1+x)*A(x)+1 = 0.

a(n) = 3F2({-n, n+1, n+2 } ; {1, 3/2})( -(1/4) ) [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]

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]

InverseSeries[Series[(y-y^2-y^3)/(1+y), {y, 0, 24}], x] (* then A(x)=y(x)/x *) - Len Smiley Apr 14 2000

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]

(Macsyma) taylor_solve_choose_order:true; taylor_solve( A^3*X^2+A^2*X+A*(X-1)+1, A, X, 0, [ 20 ]);

Cf. A007788.

Sequence in context: A076177 A007164 A126033 this_sequence A030823 A030873 A030913

Adjacent sequences: A007860 A007861 A007862 this_sequence A007864 A007865 A007866

nonn

pallo(AT)u-bourgogne.fr (Jean Pallo)