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.

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

Offset: 1

Author

Geoffrey Critzer, Sep 07 2013

Keywords

• nonn
• tabl

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.

Examples

			     2;
     2,    4;
     6,   12,    8;
    38,   60,   48,   16;
   390,  500,  360,  160,  32;
  6062, 6180, 3840, 1680, 480, 64;
  ...
		

Programs

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

Formula

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