%I A005432 M1690
%S A005432 1,1,2,6,30,156,1455,11300,151221,1694723,29594446,404126228,
%T A005432 10594925360
%N A005432 Number of permutation groups of degree n (or, number of distinct subgroups 
               of symmetric group S_n, counting conjugates as distinct).
%D A005432 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005432 J. Labelle and Y. N. Yeh, The relation between Burnside rings and combinatorial 
               species, J. Combin. Theory, A 50 (1989), 269-284.
%D A005432 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.
%D A005432 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.
%H A005432 G. Pfeiffer, <a href="http://schmidt.nuigalway.ie/subgroups">Subgroups</
               a>
%H A005432 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A005432 Exponential transform of A116655. Binomial transform of A116693. - Christian 
               G. Bower (bowerc(AT)usa.net), Feb 23 2006
%o A005432 (MAGMA) n := 5; &+[ Length(s):s in SubgroupLattice(Sym(n)) ];
%o A005432 (GAP) List([2..5],n->Sum(List(ConjugacyClassesSubgroups(SymmetricGroup(n)),
               Size))); (Hulpke)
%Y A005432 Cf. A000001, A000019. Labeled version of A000638.
%Y A005432 Sequence in context: A113593 A122763 A166078 this_sequence A009422 A057221 
               A127115
%Y A005432 Adjacent sequences: A005429 A005430 A005431 this_sequence A005433 A005434 
               A005435
%K A005432 nonn,hard,nice
%O A005432 0,3
%A A005432 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005432 a(9) and a(10) from Alexander Hulpke (hulpke(AT)math.colostate.edu), 
               Dec 03 2004
%E A005432 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.