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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).

%I A228861 #19 Apr 15 2021 20:33:50
%S A228861 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,
%T A228861 10,0,0,0,0,0,0,16807,23100,16800,7770,2331,420,35,0,0,0,0,0,0,0,
%U A228861 262144,513240,555520,412440,222936,88648,25480,5040,616,35
%N 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).
%F A228861 E.g.f.: log(A(x,y))/2 where A(x,y) is the e.g.f. for A228890.
%e A228861 Irregular Triangle begins:
%e A228861   1;
%e A228861   0, 1;
%e A228861   0, 0, 3;
%e A228861   0, 0, 0, 16,   3;
%e A228861   0, 0, 0,  0, 125,   60,   10;
%e A228861   0, 0, 0,  0,   0, 1296, 1140, 480, 105, 10;
%e A228861   ...
%t A228861 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
%Y A228861 Row sums are A001832.
%Y A228861 Cf. A002620, A228890.
%K A228861 nonn,tabf
%O A228861 1,6
%A A228861 _Geoffrey Critzer_, Sep 05 2013