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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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13
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1, 1, 2, 6, 30, 156, 1455, 11300, 151221, 1694723, 29594446, 404126228, 10594925360, 175238308453
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OFFSET
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0,3
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COMMENTS
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Up to a(12), only 2 and 1694723 are primes. [Jonathan Vos Post, Feb 6 2011].
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REFERENCES
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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.
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..13.
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, Feb 23 2006
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PROG
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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: A166078 A192446 A218940 * A009422 A057221 A180892
Adjacent sequences: A005429 A005430 A005431 * A005433 A005434 A005435
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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, Simon Plouffe
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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, Feb 23 2006 based on Goetz Pfeiffer's web page.
a(13) added by Liam Naughton, Jun 09 2011
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STATUS
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approved
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