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A241669 Irregular triangular array read by rows: T(n,k) is the number of 2-colored simple labeled graphs on n nodes that have exactly k edges, 0<=k<=A002620(n), n>=1. 0
0, 2, 2, 6, 12, 6, 14, 48, 60, 32, 6, 30, 160, 360, 440, 310, 120, 20, 62, 480, 1680, 3480, 4680, 4212, 2520, 960, 210, 20, 126, 1344, 6720, 20720, 43680, 66108, 73514, 60480, 36540, 15820, 4662, 840, 70, 254, 3584, 24192, 103040, 308560, 686784, 1172976, 1565888, 1649340, 1373680, 900592, 459312, 178416, 50960, 10080, 1232, 70, 510, 9216, 80640, 451584, 1808352, 5491584, 13102992, 25128720, 39312018, 50638224, 53981928, 47698560, 34869744, 20975472, 10281672, 4044096, 1246644, 290304, 48048, 5040, 252 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = A213441.

LINKS

Table of n, a(n) for n=1..79.

R. C. Read, The number of k-colored graphs on labelled nodes, Canad. J. Math., 12 (1960), 410—414

FORMULA

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

EXAMPLE

0,

2,  2,

6,  12,  6,

14, 48,  60,   32,   6,

30, 160, 360,  440,  310,  120,  20,

62, 480, 1680, 3480, 4680, 4212, 2520, 960, 210, 20

MATHEMATICA

nn=10; f[x_]:=Sum[x^n/(n!*(1+y)^(n^2/2)), {n, 0, nn}]; CoefficientList[Table[n!*(1+y)^(n^2/2), {n, 0, nn}]CoefficientList[Series[(f[x]-1)^2, {x, 0, nn}], x]//Simplify//Expand, y]//Grid

CROSSREFS

Sequence in context: A192933 A079005 A281351 * A178802 A156992 A285529

Adjacent sequences:  A241666 A241667 A241668 * A241670 A241671 A241672

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Aug 08 2014

STATUS

approved

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Last modified September 30 12:21 EDT 2020. Contains 337439 sequences. (Running on oeis4.)