cp's OEIS Frontend

A228892 Triangular array read by rows. T(n,k) is the number of 2-colored labeled graphs on n nodes with exactly k connected components; n>=1, 1<=k<=n.

%I A228892 #15 Feb 24 2023 15:56:42
%S A228892 2,2,4,6,12,8,38,60,48,16,390,500,360,160,32,6062,6180,3840,1680,480,
%T A228892 64,134526,109228,56280,22400,6720,1344,128,4172198,2673468,1120784,
%U A228892 384720,109760,24192,3584,256,178449270,89708004,29975400,8579424,2187360,475776,80640,9216,512,10508108222,4108881300
%N A228892 Triangular array read by rows.  T(n,k) is the number of 2-colored labeled graphs on n nodes with exactly k connected components; n>=1, 1<=k<=n.
%C A228892 A 2-colored labeled graph is a simple labeled graph in which each vertex is painted black or white and no two vertices of the same color are connected.
%C A228892 Row sums are A047863.
%C A228892 T(n,k) = A228859(n,k)*2^k.
%F A228892 E.g.f.: A(x)^y where A(x) is the e.g.f. for A047863.
%e A228892      2;
%e A228892      2,    4;
%e A228892      6,   12,    8;
%e A228892     38,   60,   48,   16;
%e A228892    390,  500,  360,  160,  32;
%e A228892   6062, 6180, 3840, 1680, 480, 64;
%e A228892   ...
%t A228892 nn=6;f[x_,y_]:=Sum[Exp[x 2^n] x^n/n!,{n,0,nn}];Map[Select[#,#>0&]&,Map[Table[#[[i]]->#[[i]]2^(i-1),{i,1,Length[#]}][[All,2]]&,Drop[Range[0,nn]!CoefficientList[Series[f[x,y]^(y/2),{x,0,nn}],{x,y}],1]]]//Grid
%K A228892 nonn,tabl
%O A228892 1,1
%A A228892 _Geoffrey Critzer_, Sep 07 2013