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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 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.)