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 A005226 Number of atomic species of degree n; also number of connected permutation groups of degree n. (Formerly M1563) 5

%I M1563

%S 0,1,1,2,6,6,27,20,130,124,598,641,4850,4772

%N Number of atomic species of degree n; also number of connected permutation groups of degree n.

%C An atomic species is one that is not the product of smaller species. - _Christian G. Bower_, Feb 23 2006

%C A permutation group is connected if it is not the direct product of smaller permutation groups. - _Christian G. Bower_, Feb 23 2006

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 147.

%D J. Labelle and Y. N. Yeh, The relation between Burnside rings and combinatorial species, J. Combin. Theory, A 50 (1989), 269-284.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D L. Naughton and G. Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F 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_, Feb 23 2006

%Y Cf. A005227. Unlabeled version of A116655.

%K nonn,more,hard

%O 0,4

%A _Simon Plouffe_

%E a(11) corrected and a(12) added by _Christian G. Bower_, Feb 23 2006 based on Goetz Pfeiffer's edit to A000638.

%E Could be extended to a(18) now using the new terms for A000637. - _N. J. A. Sloane_, Jul 30 2010

%E a(13) from _Liam Naughton_, Nov 23 2012

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