

A052395


Number of unlabeled asymmetric 4ary 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
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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 mary cacti, Advances in Applied Mathematics, 24 (2000), 2256 (pdf, dvi).
Index entries for sequences related to cacti


FORMULA

a(n) = (1/n)*(Sum_{dn} 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}] (* JeanFrançois 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



