

A034941


Number of labeled triangular cacti with 2n+1 nodes (n triangles).


6



1, 1, 15, 735, 76545, 13835745, 3859590735, 1539272109375, 831766748637825, 585243816844111425, 520038240188935042575, 569585968715180280038175, 753960950911045074462890625, 1186626209895384011075327630625, 2190213762744801162239116550679375
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200
Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the SplitDecomposition, arXiv:1608.01465 [math.CO], 2016.
Katie Gedeon, N Proudfoot, B Young, KazhdanLusztig polynomials of matroids: a survey of results and conjectures, arXiv preprint arXiv:1611.07474, 2016
Nicholas Proudfoot and Ben Young, Configuration spaces, FS^opmodules, and KazhdanLusztig polynomials of braid matroids, arXiv:1704.04510 [math.RT], 2017.
Index entries for sequences related to cacti


FORMULA

a(n) = A034940(n)/(2n+1).
The closed form a(n) = (2n1)!! (2n+1)^(n1) can be obtained from the generating function in A034940.  Noam D. Elkies, Dec 16 2002


EXAMPLE

a(3) = 5!! * 7^2 = (1*3*5) * 49 = 735.


MATHEMATICA

Table[(2n+1)^(n1)(2n)!/(2^n n!), {n, 0, 14}] (* JeanFrançois Alcover, Nov 06 2018 *)


CROSSREFS

Cf. A003081.
Sequence in context: A209461 A209523 A117812 * A199227 A055683 A196465
Adjacent sequences: A034938 A034939 A034940 * A034942 A034943 A034944


KEYWORD

nonn


AUTHOR

Christian G. Bower, Oct 15 1998


EXTENSIONS

Typo in a(10) corrected and more terms from Alois P. Heinz, Jun 23 2017


STATUS

approved



