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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
Miklos Bona, Michel Bousquet, Gilbert Labelle, and Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56.
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-François 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.
Sequence in context: A060931 A107585 A205347 * A199225 A290752 A290753
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, May 02 2018
STATUS
approved

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Last modified March 2 14:48 EST 2024. Contains 370493 sequences. (Running on oeis4.)