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A001059
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Number of doubly labeled heap-ordered trees.
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3
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1, 1, 5, 59, 1263, 42713, 2094399, 140434335, 12340275539, 1375857855221, 189751578038547, 31714568837559539, 6316261763436325285, 1477890415844440910325, 401400487846091289175217, 125247016772173387008904623, 44493481073675052201518261955
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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