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, 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

Author

Geoffrey Critzer, Aug 08 2014

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  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
		

Links

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

Crossrefs

Cf. A002620, A213441 (row sums).

Programs

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

Formula

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