A228890 Triangular array read by rows. T(n,k) is the number of 2-colored labeled graphs on n nodes with exactly k edges; n >= 0, 0 <= k <= A002620(n).

1, 2, 4, 2, 8, 12, 6, 16, 48, 60, 32, 6, 32, 160, 360, 440, 310, 120, 20, 64, 480, 1680, 3480, 4680, 4212, 2520, 960, 210, 20, 128, 1344, 6720, 20720, 43680, 66108, 73514, 60480, 36540, 15820, 4662, 840, 70, 256, 3584, 24192, 103040, 308560, 686784, 1172976, 1565888, 1649340, 1373680, 900592, 459312, 178416, 50960, 10080, 1232, 70

Offset: 0

Author

Geoffrey Critzer, Sep 07 2013

Keywords

• nonn
• tabf

Comments

A 2-colored labeled graph is a simple labeled graph in which each vertex is painted black or white and black vertices are only connected to white vertices and vice versa. [corrected by Geoffrey Critzer, Mar 27 2023]

Examples

			Triangle begins:
   1;
   2;
   4,   2;
   8,  12,    6;
  16,  48,   60,   32,    6;
  32, 160,  360,  440,  310,  120,   20;
  64, 480, 1680, 3480, 4680, 4212, 2520, 960, 210, 20;
  ...
		

Crossrefs

Row sums are A047863.

Column k=0 gives A000079.

Cf. A002620.

Programs

Mathematica

nn=6;f[x_,y_]:=Sum[Exp[x (1+y)^n]x^n/n!,{n,0,nn}];Map[Select[#,#>0&]&,Range[0,nn]!CoefficientList[Series[f[x,y],{x,0,nn}],{x,y}]]//Grid

Formula

E.g.f.: Sum_{n>=0} exp(1 + y)^n*x^n/n!