A127534 Number of jumps in all even trees with 2n edges.

0, 1, 9, 65, 442, 2940, 19380, 127281, 834900, 5476185, 35937525, 236030652, 1551652424, 10210456360, 67254204696, 443410005585, 2926078447656, 19325957314755, 127746785056275, 845069382939705, 5594334252541650

Offset: 1

Author

Emeric Deutsch, Jan 19 2007

Keywords

• nonn

Comments

An even tree is an ordered tree in which each vertex has an even outdegree. In the preorder traversal of an ordered tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump.

The Krandick reference considers jumps in full binary trees.

Links

• W. Krandick, Trees and jumps and real roots, J. Computational and Applied Math., 162, 2004, 51-55.

Crossrefs

Cf. A127535, A127536.

Programs

Maple

seq((n-1)*(4*n-3)*binomial(3*n,n)/3/(2*n+1)/(3*n-1),n=1..24);

Mathematica

Table[((n-1)(4n-3)Binomial[3n,n])/(3(2n+1)(3n-1)),{n,30}] (* Harvey P. Dale, Sep 29 2013 *)

Formula

a(n)=(n-1)(4n-3)C(3n,n)/[3(2n+1)(3n-1)].

D-finite with recurrence 8*n*(2*n+1)*a(n) -2*(136*n-69)*(n-1)*a(n-1) +5*(263*n^2-893*n+750)*a(n-2) -156*(3*n-8)*(3*n-10)*a(n-3)=0. - R. J. Mathar, Jul 22 2022