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A054367 Number of unlabeled asymmetric 6-ary cacti having n polygons. 4
1, 1, 0, 15, 110, 1095, 10326, 107056, 1149126, 12845166, 147817170, 1743640902, 20987930112, 256987965373, 3192889862238, 40171643818920, 510996955110550, 6563060603543652, 85017386945583408, 1109744672540225361, 14585261031466256370, 192882251992018723947 (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(6*d, d)) - 5*binomial(6*n, n)/(5*n+1) for n > 0. - Andrew Howroyd, May 02 2018

MATHEMATICA

a[0] = 1;

a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[6#, #]&]/n - 5 Binomial[6n, n]/(5n + 1);

Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Jul 01 2018, after Andrew Howroyd *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(6*d, d))/n - 5*binomial(6*n, n)/(5*n+1)) \\ Andrew Howroyd, May 02 2018

CROSSREFS

Column k=6 of A303913.

Cf. A054366, A054368.

Sequence in context: A060931 A107585 A205347 * A199225 A290752 A290753

Adjacent sequences:  A054364 A054365 A054366 * A054368 A054369 A054370

KEYWORD

nonn

AUTHOR

Simon Plouffe

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, May 02 2018

STATUS

approved

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Last modified February 27 11:38 EST 2021. Contains 341656 sequences. (Running on oeis4.)