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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.

Row sums are A047863.

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

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

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 November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)