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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A 2-colored labeled graph is a simple labeled graph in which each vertex is painted black or white and no black vertex is adjacent to a white vertex.

LINKS

Table of n, a(n) for n=0..58.

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

Adjacent sequences:  A228887 A228888 A228889 * A228891 A228892 A228893

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Sep 07 2013

STATUS

approved

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Last modified January 24 22:45 EST 2022. Contains 350565 sequences. (Running on oeis4.)