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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
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
0,2
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]
FORMULA
E.g.f.: Sum_{n>=0} exp(1 + y)^n*x^n/n!
EXAMPLE
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;
...
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
CROSSREFS
Row sums are A047863.
Column k=0 gives A000079.
Cf. A002620.
Sequence in context: A319252 A114593 A114655 * A051288 A120434 A319030
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Sep 07 2013
STATUS
approved