Search: id:A001187
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%I A001187 M3671 N1496
%S A001187 1,1,1,4,38,728,26704,1866256,251548592,66296291072,34496488594816,
%T A001187 35641657548953344,73354596206766622208,301272202649664088951808,
%U A001187 2471648811030443735290891264,40527680937730480234609755344896
%N A001187 Number of connected labeled graphs with n nodes.
%D A001187 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001187 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001187 D. G. Cantor, personal communication.
%D A001187 E. N. Gilbert, Enumeration of labeled graphs, Canad. J. Math., 8 (1956), 
               405-411.
%D A001187 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 
               2004; p. 518.
%D A001187 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 7.
%D A001187 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Example 5.2.1.
%D A001187 H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 78.
%H A001187 T. D. Noe, <a href="b001187.txt">Table of n, a(n) for n=0..50</a>
%H A001187 Huantian Cao, <a href="http://www.cs.uga.edu/~rwr/STUDENTS/hcao.html">
               AutoGF: An Automated System to Calculate Coefficients of Generating 
               Functions</a>.
%H A001187 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A001187 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ConnectedGraph.html">Link to a section of The World of Mathematics.</
               a>
%H A001187 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LabeledGraph.html">Link to a section of The World of Mathematics.</
               a>
%H A001187 H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</
               a>, 2nd edn., Academic Press, NY, 1994, p. 87, Eq. 3.10.2.
%H A001187 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               138
%F A001187 n*2^binomial(n, 2) = Sum_k binomial(n, k)*k*a(k)*2^binomial(n-k, 2).
%F A001187 E.g.f.: 1+log( sum(2^binomial(n, 2)*x^n/n!, n=0..infinity) ).
%p A001187 t1 := 1+log( add(2^binomial(n,2)*x^n/n!,n=0..30)): t2 := series(t1,x,
               30): A001187 := n->n!*coeff(t2,x,n);
%o A001187 (PARI) a(n)=n!*polcoeff(1+log(sum(k=0,n,2^binomial(k,2)*x^k/k!,x*O(x^n))), 
               n)
%Y A001187 Logarithmic transform of A006125 (labeled graphs). Cf. A053549.
%Y A001187 Row sums of triangle A062734.
%Y A001187 Sequence in context: A084284 A084285 A084286 this_sequence A093377 A131591 
               A030259
%Y A001187 Adjacent sequences: A001184 A001185 A001186 this_sequence A001188 A001189 
               A001190
%K A001187 nonn,nice,easy
%O A001187 0,4
%A A001187 N. J. A. Sloane (njas(AT)research.att.com).

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