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Search: id:A005226
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| A005226 |
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Number of atomic species of degree n; also number of connected permutation groups of degree n.
(Formerly M1563)
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+0
5
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| 0, 1, 1, 2, 6, 6, 27, 20, 130, 124, 598, 641, 4850
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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An atomic species is one that is not the product of smaller species. - Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006
A permutation group is connected if it is not the direct product of smaller permutation groups. - Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 147.
J. Labelle and Y. N. Yeh, The relation between Burnside rings and combinatorial species, J. Combin. Theory, A 50 (1989), 269-284.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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Inverse Euler transform of A000638. Define b(n), c(n): b(1)=c(0)=0. b(k)=A005227(k), k>1. c(k)=A000638(k), k>0. a(n) is Dirichlet convolution of b and c. - Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006
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CROSSREFS
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Cf. A005227. Unlabeled version of A116655.
Sequence in context: A100634 A130865 A105725 this_sequence A087310 A130087 A085087
Adjacent sequences: A005223 A005224 A005225 this_sequence A005227 A005228 A005229
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KEYWORD
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nonn,hard
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AUTHOR
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Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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a(11) corrected and a(12) added by Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006 based on Goetz Pfeiffer's edit to A000638.
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