login
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
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: A079005 A281351 A351081 * A356546 A178802 A156992
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Aug 08 2014
STATUS
approved