A218334 Triangular array read by rows. T(n,k) is the number of simple labeled graphs on n nodes with no isolated nodes and exactly k components. n >= 2, 1 <= k < n/2.

1, 4, 38, 3, 728, 40, 26704, 730, 15, 1866256, 20608, 420, 251548592, 961324, 12460, 105, 66296291072, 79643424, 484624, 5040, 34496488594816, 12495365424, 27712860, 220500, 945, 35641657548953344, 3844702446464, 2619965040, 11297440, 69300, 73354596206766622208, 2341246104706784, 458476648344, 775542460, 4192650, 10395

Offset

2,2

Comments

Row sums are A006129.

For even n, T(n,n/2) = A001147(n) = (2n-1)!!.

Column k = 1 is A001187.

Links

Alois P. Heinz, Rows n = 2..50, flattened

Formula

E.g.f.: exp( y*log(A(x)) ) where A(x) is the e.g.f. for A006129.

Example

                1;
                4;
               38,           3;
              728,          40;
            26704,         730,       15;
          1866256,       20608,      420;
        251548592,      961324,    12460,    105;
      66296291072,    79643424,   484624,   5040;
   34496488594816, 12495365424, 27712860, 220500, 945;

Mathematica

nn=12; a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; b=a/Exp[x]; f[list_]:=Select[list, #>0&]; Map[f, Drop[Range[0, nn]!CoefficientList[Series[Exp[y Log[b]], {x, 0, nn}], {x, y}], 2]]//Flatten

Crossrefs

Sequence in context: A027461 A144991 A073237 * A121672 A020205 A265437

Adjacent sequences: A218331 A218332 A218333 * A218335 A218336 A218337

Keyword

nonn,tabf

Author

Geoffrey Critzer, Oct 26 2012

Status

approved