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A002027 Colored graphs.
(Formerly M0365 N0138)
1
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

Table of n, a(n) for n=0..18.

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

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 *)

CROSSREFS

Essentially the same as A002031. Cf. A002032.

Sequence in context: A180069 A032185 A179236 * A290957 A032117 A137244

Adjacent sequences:  A002024 A002025 A002026 * A002028 A002029 A002030

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended by Sean A. Irvine, May 29 2013

STATUS

approved

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Last modified October 20 23:39 EDT 2018. Contains 316405 sequences. (Running on oeis4.)