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A001059 Number of labeled heap ordered trees. 2
1, 1, 5, 59, 1263, 42713, 2094399, 140434335, 12340275539, 1375857855221, 189751578038547, 31714568837559539, 6316261763436325285, 1477890415844440910325, 401400487846091289175217, 125247016772173387008904623, 44493481073675052201518261955 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

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

R. L. Grossman R. G. Larson, Hopf Algebras of Heap Ordered Trees and Permutations, arXiv:0706.1327v3 [math.RA]

Index entries for sequences related to trees

FORMULA

zf"+f'=1/(1-f).

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

Sequence in context: A020468 A093946 A249519 * A290702 A326573 A324240

Adjacent sequences:  A001056 A001057 A001058 * A001060 A001061 A001062

KEYWORD

nonn

AUTHOR

Helmut Prodinger [ Helmut.Prodinger(AT)inria.fr ]

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)