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A000638
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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)
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17
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1, 1, 2, 4, 11, 19, 56, 96, 296, 554, 1593, 3094, 10723, 20832, 75154, 159129, 686165, 1466358, 7274651
(list;
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refs;
listen;
history;
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OFFSET
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0,3
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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.
A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 91929), 1027-1079.
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, 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).
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LINKS
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Table of n, a(n) for n=0..18.
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
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FORMULA
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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
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PROG
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(MAGMA) n := 5; #SubgroupLattice(Sym(n));
(GAP 4r2) Length(ConjugacyClassesSubgroups(SymmetricGroup(n)));
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CROSSREFS
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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
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KEYWORD
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nonn,hard,more,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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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
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STATUS
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approved
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