# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a002027 Showing 1-1 of 1 %I A002027 M0365 N0138 #28 Dec 03 2018 18:27:35 %S A002027 1,2,2,6,38,390,6062,134526,4172198,178449270,10508108222, %T A002027 853219059726,95965963939958,15015789392011590,3282145108526132942, %U A002027 1005193051984479922206,432437051675617901246918,261774334771663762228012950,223306437526333657726283273822 %N A002027 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 A002027 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 A002027 R. C. Read, personal communication. %D A002027 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A002027 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A002027 Andrew Howroyd, Table of n, a(n) for n = 0..50 %H A002027 R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596. %F A002027 a(n) = m_n(2) using the functions defined in A002032. - _Sean A. Irvine_, May 29 2013 %F A002027 E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A047863. - _Geoffrey Critzer_, Sep 05 2013 %F A002027 Logarithmic transform of A047863. - _Andrew Howroyd_, Dec 03 2018 %t A002027 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 A002027 (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 A002027 Column k=2 of A322279. %Y A002027 Essentially the same as A002031. %Y A002027 Cf. A002032. %K A002027 nonn %O A002027 0,2 %A A002027 _N. J. A. Sloane_ %E A002027 Corrected and extended by _Sean A. Irvine_, May 29 2013 %E A002027 Name clarified by _Andrew Howroyd_, Dec 03 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE