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A003080 Number of rooted triangular cacti with 2n+1 nodes (n triangles).
(Formerly M1448)
4
1, 1, 2, 5, 13, 37, 111, 345, 1105, 3624, 12099, 41000, 140647, 487440, 1704115, 6002600, 21282235, 75890812, 272000538, 979310627, 3540297130, 12845634348, 46764904745, 170767429511, 625314778963, 2295635155206, 8447553316546, 31153444946778, 115122389065883 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 305, (4.2.34).

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 73, (3.4.20).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1 (1992) pp. 53-80.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)

N. J. A. Sloane, Transforms

Index entries for sequences related to cacti

FORMULA

a(n)=b(2n+1). b shifts left under transform T where Tb = EULER(E_2(b)). E_2(b) has g.f. (B(x^2)+B(x)^2)/2.

MATHEMATICA

terms = 30;

nmax = 2 terms;

A[_] = 0; Do[A[x_] = x Exp[Sum[(A[x^n]^2 + A[x^(2n)])/(2n), {n, 1, terms}]] + O[x]^nmax // Normal, {nmax}];

DeleteCases[CoefficientList[A[x], x], 0] (* Jean-François Alcover, Sep 02 2018 *)

CROSSREFS

Cf. A003081, A034940, A034941.

Sequence in context: A151416 A193114 A114509 * A149854 A151442 A263529

Adjacent sequences:  A003077 A003078 A003079 * A003081 A003082 A003083

KEYWORD

nonn,eigen,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Sequence extended by Paul Zimmermann, Mar 15 1996

Additional comments from Christian G. Bower

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)