This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 W. Lang, First 6 rows. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)