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A054422 Number of unlabeled asymmetric ternary cacti having n triangles. 4
1, 1, 0, 3, 10, 54, 222, 1107, 5346, 27399, 142770, 764967, 4170672, 23140813, 130189302, 741650172, 4270501218, 24825326196, 145534796520, 859627488963, 5112003992610, 30586307195304, 184023393204654, 1112800162657899 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Miklos Bona, Michel Bousquet, Gilbert Labelle, Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56 (pdf, dvi).

Index entries for sequences related to cacti

FORMULA

a(n) = (1/n)*(Sum_{d|n} mu(n/d)*binomial(3*d, d)) - 2*binomial(3*n, n)/(2*n+1) for n > 0. - Andrew Howroyd, May 02 2018

MATHEMATICA

a[0] = 1; a[n_] := (1/n) Sum[MoebiusMu[n/d] Binomial[3d, d], {d, Divisors[n] } ] - 2 Binomial[3n, n]/(2n + 1);

Table[a[n], {n, 0, 23}] (* Jean-Fran├žois Alcover, Jul 24 2018, after Andrew Howroyd *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(3*d, d))/n - 2*binomial(3*n, n)/(2*n+1)) \\ Andrew Howroyd, May 02 2018

CROSSREFS

Column k=3 of A303913.

Cf. A052393, A054423.

Sequence in context: A199202 A135829 A071895 * A074503 A318188 A229311

Adjacent sequences:  A054419 A054420 A054421 * A054423 A054424 A054425

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe Mar 15 2000

EXTENSIONS

More terms from James A. Sellers, Mar 16 2000.

STATUS

approved

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Last modified October 20 18:19 EDT 2019. Contains 328269 sequences. (Running on oeis4.)