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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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5
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0, 1, 1, 2, 6, 6, 27, 20, 130, 124, 598, 641, 4850
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| 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
| Cf. A005227. Unlabeled version of A116655.
Sequence in context: A100634 A130865 A105725 * A087310 A130087 A085087
Adjacent sequences: A005223 A005224 A005225 * A005227 A005228 A005229
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KEYWORD
| nonn,hard
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| 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.
Could be extended to a(18) now using the new terms for A000637. - N. J. A. Sloane, Jul 30 2010
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