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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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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: A055695 A113593 A122763 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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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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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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