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A054367
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Number of unlabeled asymmetric 6-ary cacti having n polygons.
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4
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1, 1, 0, 15, 110, 1095, 10326, 107056, 1149126, 12845166, 147817170, 1743640902, 20987930112, 256987965373, 3192889862238, 40171643818920, 510996955110550, 6563060603543652, 85017386945583408, 1109744672540225361, 14585261031466256370, 192882251992018723947
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OFFSET
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0,4
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LINKS
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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
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FORMULA
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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
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MATHEMATICA
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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-François Alcover, Jul 01 2018, after Andrew Howroyd *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe
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EXTENSIONS
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Terms a(11) and beyond from Andrew Howroyd, May 02 2018
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STATUS
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approved
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