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%I M0365 N0138 #28 Dec 03 2018 18:27:35
%S 1,2,2,6,38,390,6062,134526,4172198,178449270,10508108222,
%T 853219059726,95965963939958,15015789392011590,3282145108526132942,
%U 1005193051984479922206,432437051675617901246918,261774334771663762228012950,223306437526333657726283273822
%N Number of connected graphs on n labeled nodes, each node being colored with one of 2 colors, such that no edge joins nodes of the same color.
%C a(n) is the number of connected labeled graphs with n 2-colored nodes where black nodes are only connected to white nodes and vice versa. - _Geoffrey Critzer_, Sep 05 2013
%D R. C. Read, personal communication.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A002027/b002027.txt">Table of n, a(n) for n = 0..50</a>
%H R. C. Read, E. M. Wright, <a href="http://dx.doi.org/10.4153/CJM-1970-066-1">Colored graphs: A correction and extension</a>, Canad. J. Math. 22 1970 594-596.
%F a(n) = m_n(2) using the functions defined in A002032. - _Sean A. Irvine_, May 29 2013
%F E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A047863. - _Geoffrey Critzer_, Sep 05 2013
%F Logarithmic transform of A047863. - _Andrew Howroyd_, Dec 03 2018
%t nn=10;f[x_]:=Sum[Sum[Binomial[n,k]2^(k(n-k)),{k,0,n}]x^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[Log[f[x]]+1,{x,0,nn}],x] (* _Geoffrey Critzer_, Sep 05 2013 *)
%o (PARI) seq(n)={Vec(serlaplace(1 + log(serconvol(sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n), (sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n))^2))))} \\ _Andrew Howroyd_, Dec 03 2018
%Y Column k=2 of A322279.
%Y Essentially the same as A002031.
%Y Cf. A002032.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E Corrected and extended by _Sean A. Irvine_, May 29 2013
%E Name clarified by _Andrew Howroyd_, Dec 03 2018
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