cp's OEIS Frontend

A005226 Number of atomic species of degree n; also number of connected permutation groups of degree n.

%I A005226 M1563 #57 Mar 17 2020 04:37:38
%S A005226 0,1,1,2,6,6,27,20,130,124,598,641,4850,4772,35625,46074,389839,
%T A005226 487408,4617554
%N A005226 Number of atomic species of degree n; also number of connected permutation groups of degree n.
%C A005226 An atomic species is one that is not the product of smaller species. - _Christian G. Bower_, Feb 23 2006
%C A005226 A permutation group is connected if it is not the direct product of smaller permutation groups. - _Christian G. Bower_, Feb 23 2006
%D A005226 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 147.
%D A005226 Jacques Labelle, Quelques espèces sur les ensembles de petite cardinalité, Ann. Sc. Math. Québec 9.1 (1985): 31-58.
%D A005226 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005226 H. Decoste, G. Labelle & J. Labelle, <a href="/A005226/a005226.pdf">Espèces sur les petites cardinalités Tableaux divers</a>, Université du Québec à Montréal (octobre 1988), Unpublished.
%H A005226 Jacques Labelle, <a href="/A005226/a005226_1.pdf">Quelques espèces sur les ensembles de petite cardinalité</a>, Ann. Sc. Math. Québec 9.1 (1985): 31-58. (Annotated scanned copy of preprint)
%H A005226 J. Labelle and Y. N. Yeh, <a href="http://dx.doi.org/10.1016/0097-3165(89)90019-8">The relation between Burnside rings and combinatorial species</a>, J. Combin. Theory, A 50 (1989), 269-284.
%H A005226 L. Naughton and G. Pfeiffer, <a href="http://arxiv.org/abs/1211.1911">Integer sequences realized by the subgroup pattern of the symmetric group</a>, arXiv:1211.1911 [math.GR], 2012-2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Naughton/naughton2.html">J. Int. Seq. 16 (2013) #13.5.8</a>.
%H A005226 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A005226 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
%t A005226 A000638 = Cases[Import["https://oeis.org/A000638/b000638.txt", "Table"], {_, _}][[All, 2]];
%t A005226 (* EulerInvTransform is defined in A022562 *)
%t A005226 {0} ~Join~ EulerInvTransform[A000638 // Rest] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)
%Y A005226 Cf. A005227. Unlabeled version of A116655.
%K A005226 nonn,more,hard
%O A005226 0,4
%A A005226 _Simon Plouffe_
%E A005226 a(11) corrected and a(12) added by _Christian G. Bower_, Feb 23 2006 based on Goetz Pfeiffer's edit to A000638.
%E A005226 Could be extended to a(18) now using the new terms for A000637. - _N. J. A. Sloane_, Jul 30 2010
%E A005226 a(13) from _Liam Naughton_, Nov 23 2012
%E A005226 a(14)-a(18) from the inverse Euler transform of A000637. - _R. J. Mathar_, Mar 03 2015