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

0,3

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Connected Component

Formula

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

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}]]

Crossrefs

Sequence in context: A183120 A100702 A367484 * A147586 A305197 A071716

Adjacent sequences: A224028 A224029 A224030 * A224032 A224033 A224034

Keyword

nonn

Author

Geoffrey Critzer, Mar 30 2013

Status

approved