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A131449 Number of organic (also called increasing) vertex labelings of rooted ordered trees with n non-root vertices. 1
1, 1, 2, 1, 6, 3, 3, 2, 1, 24, 12, 12, 12, 8, 8, 6, 6, 4, 4, 3, 3, 2, 1, 120, 60, 60, 60, 60, 40, 40, 40, 30, 30, 30, 30, 30, 24, 20, 20, 20, 20, 20, 15, 15, 15, 15, 12, 12, 12, 10, 10, 10, 10, 8, 8, 6, 6, 5, 5, 4, 4, 3, 3, 2, 1, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Organic vertex labeling with numbers 1,2,...,n means that the sequence of vertex labels along the (unique) path from the root with label 0 to any leaf (non-root vertex of degree 1) is increasing.

Row lengths sequence, i.e. the number of rooted ordered trees, C(n):=A000108(n) (Catalan numbers): [1,1,2,5,14,42,...].

Number of rooted trees with n non-root vertices [1,1,2,4,9,20,...]=A000081(n+1).

Row sums give [1,1,3,155,105,945,...]= A001147(n), n>=0. A035342(n,1), n>=1, first column of triangle S2(3).

LINKS

Table of n, a(n) for n=0..65.

W. Lang, First 6 rows.

W. Lang, Rooted ordered trees with n=5 non-root vertices and number of labelings.

EXAMPLE

[0! ]; [1! ]; [2!,1]; [3!,3,3,2,1], [4!,12,12,12,8,8,6,6,4,4,3,3,2,1];...

n=3: 3 labelings (0,1,2)(0,3), (0,1,3) (0,2) and (0,2,3) (0,1) for the rooted tree o-o-x-o.

n=3: 3 labelings (0,3)(0,1,2), (0,2)(0,1,3) and (0,1)(0,2,3) for the rooted tree o-x-o-o.

CROSSREFS

Sequence in context: A165908 A121281 A232467 * A289869 A124443 A077172

Adjacent sequences:  A131446 A131447 A131448 * A131450 A131451 A131452

KEYWORD

nonn,more,tabf

AUTHOR

Wolfdieter Lang Aug 07 2007

STATUS

approved

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Last modified February 24 21:30 EST 2018. Contains 299628 sequences. (Running on oeis4.)