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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)
17
1, 1, 2, 4, 11, 19, 56, 96, 296, 554, 1593, 3094, 10723, 20832, 75154, 159129, 686165, 1466358, 7274651 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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

A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 91929), 1027-1079.

G. Pfeiffer, Counting Transitive Relations, preprint 2004.

C. C. Sims, Computational methods in the study of permutation groups, pp. 169-183 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.

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

G. Pfeiffer, Subgroups

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

N. J. A. Sloane, Transforms

G. Xiao, PermGroup

FORMULA

Euler Transform of A005226. Define b(n), c(n): b(1)=c(0)=0. b(k)=A005227(k), k>1. c(k)=a(k), k>0. A005226(n) 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

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

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Last modified April 18 19:18 EDT 2014. Contains 240733 sequences.