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

1,2

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: A079005 A281351 A351081 * A356546 A178802 A156992

Adjacent sequences: A241666 A241667 A241668 * A241670 A241671 A241672

Keyword

nonn,tabf

Author

Geoffrey Critzer, Aug 08 2014

Status

approved