

A000638


Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n.
(Formerly M1244 N0477)


18



1, 1, 2, 4, 11, 19, 56, 96, 296, 554, 1593, 3094, 10723, 20832, 75154, 159129, 686165, 1466358, 7274651
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OFFSET

0,3


REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and TreeLike Structures, Camb. 1998, p. 147.
Labelle, Jacques. "Quelques especes sur les ensembles de petite cardinalité."Ann. Sc. Math. Québec 9.1 (1985): 3158.
G. Pfeiffer, Counting Transitive Relations, preprint 2004.
C. C. Sims, Computational methods in the study of permutation groups, pp. 169183 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..18.
D. Holt, Enumerating subgroups of the symmetric group, in Computational Group Theory and the Theory of Groups, II, edited by L.C. Kappe, A. Magidin and R. Morse. AMS Contemporary Mathematics book series, vol. 511, pp. 3337. [Annotated copy]
A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 10271079.
A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 10271079. [Annotated scan of page 1069 only]
L. Naughton and G. Pfeiffer, Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group, arXiv preprint arXiv:1211.1911, 2012.  From N. J. A. Sloane, Jan 02 2013
Götz Pfeiffer, Numbers of subgroups of various families of groups
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
C. C. Sims, Letter to N. J. A. Sloane (no date)
N. J. A. Sloane, Transforms
G. Xiao, PermGroup
Index entries for sequences related to groups


FORMULA

Euler Transform of A005226. Define b(n), c(n), d(n): b(1)=d(1)=0. b(k)=A005227(k), k>1. c(k)=a(k), k>0, d(k)=A005226(k), k>1. d is Dirichlet convolution of b and c.  Christian G. Bower, Feb 23 2006


PROG

(MAGMA) n := 5; #SubgroupLattice(Sym(n));
(GAP 4r2) Length(ConjugacyClassesSubgroups(SymmetricGroup(n)));


CROSSREFS

Partial sums of A000637.
Cf. A000001, A000019. Unlabeled version of A005432.
Sequence in context: A018674 A076518 A139785 * A039824 A204519 A076636
Adjacent sequences: A000635 A000636 A000637 * A000639 A000640 A000641


KEYWORD

nonn,hard,more,nice,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(11) corrected and a(12) added by Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004
Extended to a(18) using Derek Holt's data from A000637.  N. J. A. Sloane, Jul 31 2010


STATUS

approved



