A224031 Number of connected components over all simple unlabeled graphs with n nodes.

0, 1, 3, 7, 19, 55, 222, 1303, 13845, 289796, 12309107, 1031600490, 166135132131, 50669199124597, 29104991031790932, 31455641633255556350, 64032500451659605651790, 245999928109779646497947269, 1787823789106309664923287885113

Offset: 0

Author

Geoffrey Critzer, Mar 30 2013

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Connected Component

Programs

Mathematica

nn=15; f[list_] := Total[Table[list[[i]]*(i-1), {i,1,Length[list]}]]; g[x_]:=Sum[NumberOfGraphs[n]x^n,{n,0,nn}]; c[x_]:=Sum[a[n]x^n,{n,0,nn}]; a[0]=1; sol=SolveAlways[g[x]==Normal[Series[Product[1/(1-x^i)^a[i], {i,1,nn}], {x,0,nn}]], x]; b=Drop[Flatten[Table[a[n],{n,0,nn}]/.sol],1]; Map[f,CoefficientList[Series[Product[1/(1-y x^i)^b[[i]], {i,1,nn}], {x,0,nn}], {x,y}]]

Formula

Sum_{m=1..n} A201922(m,n).