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Search: id:A054365
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| A054365 |
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Number of unlabeled 5-gonal cacti having n polygons. |
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+0
1
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| 1, 1, 1, 3, 17, 102, 811, 6626, 58385, 532251, 5011934, 48344880, 475982471, 4766639628, 48434621610, 498363430232, 5184274255789, 54451326151253, 576810990484823, 6156943228387305, 66170786572330174, 715564777086617766
(list; graph; listen)
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OFFSET
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0,4
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LINKS
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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
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MAPLE
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with(combinat): with(numtheory): m := 5: for p from 2 to 28 do s1 := 0: s2 := 0: for d from 1 to p do if p mod d = 0 then s1 := s1+phi(p/d)*binomial(m*d, d) fi: od: for d from 1 to p-1 do if gcd(m, p-1) mod d = 0 then s2 := s2+phi(d)*binomial((p*m)/d, (p-1)/d) fi: od: printf(`%d, `, (s1+s2)/(m*p)-binomial(m*p, p)/(p*(m-1)+1)) od:
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CROSSREFS
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Sequence in context: A001541 A161940 A074565 this_sequence A116886 A163064 A020069
Adjacent sequences: A054362 A054363 A054364 this_sequence A054366 A054367 A054368
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms and Maple program from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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