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 A228892 Triangular array read by rows.  T(n,k) is the number of 2-colored labeled graphs on n nodes with exactly k connected components; n>=1, 1<=k<=n. 0
 2, 2, 4, 6, 12, 8, 38, 60, 48, 16, 390, 500, 360, 160, 32, 6062, 6180, 3840, 1680, 480, 64, 134526, 109228, 56280, 22400, 6720, 1344, 128, 4172198, 2673468, 1120784, 384720, 109760, 24192, 3584, 256, 178449270, 89708004, 29975400, 8579424, 2187360, 475776, 80640, 9216, 512, 10508108222, 4108881300 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A 2-colored labeled graph is a simple labeled graph in which each vertex is painted black or white and no two vertices of the same color are connected. Row sums are A047863. T(n,k) = A228859(n,k)2^k. LINKS FORMULA E.g.f.: A(x)^y where A(x) is the e.g.f. for A047863. EXAMPLE 2, 2, 4, 6, 12, 8, 38, 60, 48, 16, 390, 500, 360, 160, 32, 6062, 6180, 3840, 1680, 480, 64 MATHEMATICA nn=6; f[x_, y_]:=Sum[Exp[x 2^n] x^n/n!, {n, 0, nn}]; Map[Select[#, #>0&]&, Map[Table[#[[i]]#[[i]]2^(i-1), {i, 1, Length[#]}][[All, 2]]&, Drop[Range[0, nn]!CoefficientList[Series[f[x, y]^(y/2), {x, 0, nn}], {x, y}], 1]]]//Grid CROSSREFS Sequence in context: A278246 A195204 A318847 * A267610 A336940 A291365 Adjacent sequences:  A228889 A228890 A228891 * A228893 A228894 A228895 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Sep 07 2013 STATUS approved

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Last modified January 29 04:22 EST 2022. Contains 350672 sequences. (Running on oeis4.)