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A091486 Number of unlabeled rooted 2,3 cacti (triangular cacti with bridges). 4
1, 1, 3, 7, 21, 60, 190, 600, 1977, 6589, 22408, 77050, 268178, 941599, 3333585, 11882427, 42615480, 153653039, 556664752, 2025330509, 7397242875, 27111563026, 99681629658, 367563272278, 1358945378906, 5036549490009, 18708739990129, 69640873691941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also number of unlabeled involution rooted trees.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

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

N. J. A. Sloane, Transforms

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

FORMULA

Shifts left under transform T where Ta = EULER(E_1, 2(a)). E_1, 2(a) has g.f. A(x)+(A(x^2)+A(x)^2)/2.

PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(EulerT(Vec(p + (p^2 + subst(p, x, x^2))/2))))); Vec(p)} \\ Andrew Howroyd, Aug 30 2018

CROSSREFS

Cf. A091487, A091488.

Sequence in context: A182887 A035080 A229188 * A056779 A183113 A102877

Adjacent sequences:  A091483 A091484 A091485 * A091487 A091488 A091489

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Jan 14 2004

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)