A218696 - OEIS

%I #8 Nov 04 2012 16:16:28

%S 1,15,222,3680,69345,1477182,35234220,932070708,27109785510,

%T 860394764515,29600058300780,1097511032533500,43637308561557074,

%U 1852311640075120980,83612841417061582320,3999611090385007608840,202111299843794061251580,10758947714752854861908379

%N Number of components over all graphs on n labeled nodes with unicyclic components (graphs counted by A137916).

%H Alois P. Heinz, <a href="/A218696/b218696.txt">Table of n, a(n) for n = 3..150</a>

%F a(n) = Sum_{m=1..floor(n/3)} A106239(n,m)*m.

%t nn=22;t=Sum[n^(n-1)x^n/n!,{n,1,nn}];Drop[Range[0,nn]!CoefficientList[ Series[D[Exp[y(Log[1/(1-t)]/2-t/2-t^2/4)],y]/.y->1,{x,0,nn}],x],3]

%Y Cf. A057500.

%K nonn

%O 3,2

%A _Geoffrey Critzer_, Nov 04 2012