OFFSET
1,3
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.
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jan 19 2007
STATUS
approved