0,3

A minimax tree is i) rooted ii) binary (i.e. each node has at most two sons) iii) topological (i.e. the left son is different from the right son) iv) labeled (i.e. there is a bijection between the nodes and a finite totally ordered set). Moreover it has the following property v) the label of each node x is the minimum or the maximum of all the labels of the nodes of the subtree whose root is x.

Dominique Foata and Guo-Niu Han, Arbres minimax et polynomes d'Andre. Special issue in honor of Dominique Foata's 65th birthday (Philadelphia, PA, 2000). Adv. in Appl. Math. 27 (2001), no. 2-3, 367-389.

Dominique Foata & Guo-Niu Han, Arbres minimax et polynomes d'Andre , Advances in Appl. Math., 27, 2001, p. 367-389.

E.g.f.: ( Tanh( ArcTanh(Sqrt(2)) - Sqrt(2) x ) )/Sqrt(2) = Sqrt(2)/2 ( 1 + ( 3 - 2 Sqrt(2) ) Exp( 2 Sqrt(2) x ) )/( 1 - ( 3 - 2 Sqrt(2) ) Exp( 2 Sqrt(2) x ) ). Recurrence: a(n+1) = 2 Sum_{k=0..n} binomial(n,k)*a(k)*a(n-k)) - 0^n.

a(2n) = 2^n * A006154(2n), n>0 (conjectured). - R. Stephan, Apr 29 2004

For n>0, a(n)=sqrt(2)^(3*n+1)*sum(k=0, infty, k^n/(1+sqrt(2))^(2*k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 12 2005

Sequence in context: A151341 A135886 A007550 this_sequence A126674 A082032 A140585

Adjacent sequences: A080792 A080793 A080794 this_sequence A080796 A080797 A080798

nonn

Emanuele Munarini (munarini(AT)mate.polimi.it), Mar 14 2003