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A052395 Number of unlabeled asymmetric 4-ary cacti having n polygons. 4
1, 1, 0, 6, 28, 193, 1140, 7688, 52364, 373560, 2732836, 20506254, 156899748, 1221179922, 9642327324, 77092881840, 623120435820, 5085013101160, 41850590485164, 347060754685884, 2897800074184240, 24344668688255109, 205667186830447412, 1746375819789491992 (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 and 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(4*d, d)) - 3*binomial(4*n, n)/(3*n+1) for n > 0. - Andrew Howroyd, Apr 30 2018

MATHEMATICA

a[0] = 1;

a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[4#, #]&]/n - 3 Binomial[4n, n]/(3n + 1);

Table[a[n], {n, 0, 23}] (* Jean-Fran├žois Alcover, Jun 29 2018, after Andrew Howroyd *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(4*d, d))/n - 3*binomial(4*n, n)/(3*n+1)) \\ Andrew Howroyd, Apr 30 2018

CROSSREFS

Column k=4 of A303913.

Cf. A052394, A054362.

Sequence in context: A173081 A278015 A169723 * A034660 A206708 A216413

Adjacent sequences:  A052392 A052393 A052394 * A052396 A052397 A052398

KEYWORD

nonn

AUTHOR

Simon Plouffe

EXTENSIONS

Terms a(13) and beyond from Andrew Howroyd, May 02 2018

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)