A228861 Irregular triangular array read by rows. T(n,k) is the number of connected labeled bipartite graphs on n nodes with exactly k edges; n >= 1, 0 <= k <= A002620(n+1).

1, 0, 1, 0, 0, 3, 0, 0, 0, 16, 3, 0, 0, 0, 0, 125, 60, 10, 0, 0, 0, 0, 0, 1296, 1140, 480, 105, 10, 0, 0, 0, 0, 0, 0, 16807, 23100, 16800, 7770, 2331, 420, 35, 0, 0, 0, 0, 0, 0, 0, 262144, 513240, 555520, 412440, 222936, 88648, 25480, 5040, 616, 35

Offset: 1

Author

Geoffrey Critzer, Sep 05 2013

Keywords

• nonn
• tabf

Examples

			Irregular Triangle begins:
  1;
  0, 1;
  0, 0, 3;
  0, 0, 0, 16,   3;
  0, 0, 0,  0, 125,   60,   10;
  0, 0, 0,  0,   0, 1296, 1140, 480, 105, 10;
  ...
		

Crossrefs

Row sums are A001832.

Cf. A002620, A228890.

Programs

Mathematica

nn=8;f[x_,y_]:=Sum[Sum[Binomial[n,k](1+y)^(k(n-k)),{k,0,n}]x^n/n!,{n,0,nn}];Table[PadLeft[a=Map[Select[#,#>0&]&,Drop[Range[0,nn]!CoefficientList[Series[Log[f[x,y]]/2,{x,0,nn}],{x,y}],1]][[n]],Length[a]+n-1],{n,1,nn}]//Grid

Formula

E.g.f.: log(A(x,y))/2 where A(x,y) is the e.g.f. for A228890.