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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

%I

%S 2,2,4,6,12,8,38,60,48,16,390,500,360,160,32,6062,6180,3840,1680,480,

%T 64,134526,109228,56280,22400,6720,1344,128,4172198,2673468,1120784,

%U 384720,109760,24192,3584,256,178449270,89708004,29975400,8579424,2187360,475776,80640,9216,512,10508108222,4108881300

%N 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.

%C 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.

%C Row sums are A047863.

%C T(n,k) = A228859(n,k)2^k.

%F E.g.f.: A(x)^y where A(x) is the e.g.f. for A047863.

%e 2,

%e 2, 4,

%e 6, 12, 8,

%e 38, 60, 48, 16,

%e 390, 500, 360, 160, 32,

%e 6062, 6180, 3840, 1680, 480, 64

%t 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

%K nonn,tabl

%O 1,1

%A _Geoffrey Critzer_, Sep 07 2013

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)