Search: id:A000684
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%I A000684 M2954 N1192
%S A000684 1,3,13,81,721,9153,165313,4244481,154732801,8005686273,
%T A000684 587435092993,61116916981761,9011561121239041,1882834327457349633,
%U A000684 557257804202631217153,233610656002563147038721,138681207656726645785559041
%N A000684 Number of colored labeled n-node graphs with 2 interchangeable colors.
%D A000684 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000684 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000684 F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 
               31 (1979), 60-68.
%D A000684 D. A. Klarner, The number of graded partially ordered sets, J. Combin. 
               Theory, 6 (1969), 12-19.
%D A000684 A. Nymeyer and R. W. Robinson, ``Tabulation of the Numbers of Labeled 
               Bipartite Blocks and Related Classes of Bicolored Graphs,'' unpublished 
               manuscript, 1982.
%D A000684 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%H A000684 R. W. Robinson, <a href="b000684.txt">Table of n, a(n) for n = 1..32</
               a>
%H A000684 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Bipartite, k-colorable 
               and k-colored graphs</a> (2*A000684)
%F A000684 G.f.: A(x) = Sum_{n>=1} x^n/(1 - 2^n*x)^n. [From Paul D. Hanna (pauldhanna(AT)juno.com), 
               Sep 14 2009]
%o A000684 (PARI) a(n)=polcoeff(sum(k=1,n,x^k/(1-2^k*x +x*O(x^n))^k),n) [From Paul 
               D. Hanna (pauldhanna(AT)juno.com), Sep 14 2009]
%Y A000684 2 * A000683(n) + 1. Cf. A058872.
%Y A000684 Sequence in context: A135921 A005923 A089461 this_sequence A057993 A000904 
               A135743
%Y A000684 Adjacent sequences: A000681 A000682 A000683 this_sequence A000685 A000686 
               A000687
%K A000684 nonn,nice,easy
%O A000684 1,2
%A A000684 N. J. A. Sloane (njas(AT)research.att.com).
%E A000684 a(15) onwards added by N. J. A. Sloane (njas(AT)research.att.com), Oct 
               19 2006 from the Robinson reference

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