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%I #12 Aug 28 2013 05:03:53
%S 1,1,2,4,48,944,32288,2089312,268215040,68708556288,35183367427072,
%T 36028619925285888,73786915826515503104,302231414653310649337856,
%U 2475880026112961032035266560,40564819073011099018919903485952,1329227995107917459000217502447435776
%N The number of simple labeled graphs on n nodes with no components of size 3.
%H Alois P. Heinz, <a href="/A228596/b228596.txt">Table of n, a(n) for n = 0..50</a>
%F E.g.f.: exp(-4*x^3/3!)*A(x) where A(x) is the e.g.f. for A006125.
%F Generally, the e.g.f. for the number of simple labeled graphs on n nodes with no size k components is exp( -A001187(k)*x^k/k! ) * A(x) with A(x) as above.
%t nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
%t Range[0, nn]! CoefficientList[Series[Exp[-4 x^3/3!] g, {x, 0, nn}], x]
%Y Cf. A093352, A006129.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Aug 27 2013