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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.
(Formerly M0365 N0138)
5
1, 2, 2, 6, 38, 390, 6062, 134526, 4172198, 178449270, 10508108222, 853219059726, 95965963939958, 15015789392011590, 3282145108526132942, 1005193051984479922206, 432437051675617901246918, 261774334771663762228012950, 223306437526333657726283273822 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
REFERENCES
R. C. Read, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596.
FORMULA
a(n) = m_n(2) using the functions defined in A002032. - Sean A. Irvine, May 29 2013
E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A047863. - Geoffrey Critzer, Sep 05 2013
Logarithmic transform of A047863. - Andrew Howroyd, Dec 03 2018
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Column k=2 of A322279.
Essentially the same as A002031.
Cf. A002032.
Sequence in context: A180069 A032185 A179236 * A290957 A032117 A137244
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by Sean A. Irvine, May 29 2013
Name clarified by Andrew Howroyd, Dec 03 2018
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)