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

1,6

Links

Table of n, a(n) for n=1..58.

Formula

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

Example

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;
  ...

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

Crossrefs

Row sums are A001832.

Cf. A002620, A228890.

Sequence in context: A057389 A241668 A377127 * A057382 A007270 A222896

Adjacent sequences: A228858 A228859 A228860 * A228862 A228863 A228864

Keyword

nonn,tabf

Author

Geoffrey Critzer, Sep 05 2013

Status

approved