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Search: id:A005432
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| A005432 |
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Number of permutation groups of degree n (or, number of distinct subgroups of symmetric group S_n, counting conjugates as distinct).
(Formerly M1690)
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+0
11
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| 1, 1, 2, 6, 30, 156, 1455, 11300, 151221, 1694723, 29594446, 404126228, 10594925360
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Labelle and Y. N. Yeh, The relation between Burnside rings and combinatorial species, J. Combin. Theory, A 50 (1989), 269-284.
L. Pyber, Ann. Math. 137 (1993), 203-220 shows c^{n^2(1+o(1))} <= a(n) <= d^{n^2(1+o(1)}, c=2^{1/16}, d=24^{1/6}; conjectures lower bound is accurate.
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.
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LINKS
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G. Pfeiffer, Subgroups
N. J. A. Sloane, Transforms
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FORMULA
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Exponential transform of A116655. Binomial transform of A116693. - Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006
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PROGRAM
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(MAGMA) n := 5; &+[ Length(s):s in SubgroupLattice(Sym(n)) ];
(GAP) List([2..5], n->Sum(List(ConjugacyClassesSubgroups(SymmetricGroup(n)), Size))); (Hulpke)
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CROSSREFS
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Cf. A000001, A000019. Labeled version of A000638.
Sequence in context: A113593 A122763 A166078 this_sequence A009422 A057221 A127115
Adjacent sequences: A005429 A005430 A005431 this_sequence A005433 A005434 A005435
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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a(9) and a(10) from Alexander Hulpke (hulpke(AT)math.colostate.edu), Dec 03 2004
More terms from a(11) and a(12) added by Christian G. Bower (bowerc(AT)usa.net), Feb 23 2006 based on Goetz Pfeiffer's web page.
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