A001059 Number of doubly labeled heap-ordered trees.

1, 1, 5, 59, 1263, 42713, 2094399, 140434335, 12340275539, 1375857855221, 189751578038547, 31714568837559539, 6316261763436325285, 1477890415844440910325, 401400487846091289175217, 125247016772173387008904623, 44493481073675052201518261955

Offset

0,3

Comments

A standard heap-ordered tree with n+1 nodes is a finite rooted tree in which all the nodes except the root are labeled with the natural numbers between 1 and n, which satisfies the property that the labels of the children of a node are all larger than the label of the node.

Rooted trees counted by a(n) have n non-root vertices with two independent heap ordering labelings. The number of standard heap-ordered trees with n non-root vertices is A001147(n). - Andrey Zabolotskiy, Sep 16 2022

Links

T. D. Noe, Table of n, a(n) for n = 0..100

R. L. Grossman and R. G. Larson, Hopf Algebras of Heap Ordered Trees and Permutations, arXiv:0706.1327 [math.RA], 2007.

Index entries for sequences related to trees

Formula

Doubly exponential generating function f(z) = Sum_{n>=0} a(n+1) z^n/n!^2 satisfies zf"+f'=1/(1-f). [Clarified by Andrey Zabolotskiy, Sep 16 2022]

a(n) = Sum_{k=0..n-1} binomial(n, k)^2*a(k)*a(n-k-1). - Vladeta Jovovic, Oct 22 2005

Mathematica

t = {1}; Do[AppendTo[t, Sum[Binomial[n, k]^2 t[[k+1]] t[[n-k]], {k, 0, n-1}]], {n, 20}] (* T. D. Noe, Jun 25 2012 *)

Crossrefs

Cf. A001147.

Sequence in context: A093946 A249519 A371327 * A290702 A046842 A348181

Adjacent sequences: A001056 A001057 A001058 * A001060 A001061 A001062

Keyword

nonn

Author

Helmut Prodinger

Extensions

Name edited by Andrey Zabolotskiy, Sep 16 2022

Status

approved