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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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6
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0, 1, 1, 2, 6, 6, 27, 20, 130, 124, 598, 641, 4850, 4772, 35625, 46074, 389839, 487408, 4617554
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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An atomic species is one that is not the product of smaller species. - Christian G. Bower, Feb 23 2006
A permutation group is connected if it is not the direct product of smaller permutation groups. - Christian G. Bower, 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.
Jacques Labelle, Quelques espèces sur les ensembles de petite cardinalité, Ann. Sc. Math. Québec 9.1 (1985): 31-58.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Inverse Euler transform of A000638. Define b(n), c(n), d(): b(1)=d(1)=0. b(k)=A005227(k), k>1. c(k)=A000638(k), k>0. d(k)=a(k), k>1. d is Dirichlet convolution of b and c. - Christian G. Bower, Feb 23 2006
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MATHEMATICA
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A000638 = Cases[Import["https://oeis.org/A000638/b000638.txt", "Table"], {_, _}][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{0} ~Join~ EulerInvTransform[A000638 // Rest] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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