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%I #13 Jul 22 2019 20:49:32
%S 0,137,1267,6412,23597,70707,183099,424809,904299,1795794,3367364,
%T 6017011,10318126,17075786,27395466,42765846,65157498,97139343,
%U 142014873,203980238,288306403,401547685,551779085,748864935,1004761485,1333856160,1753346322,2283660477
%N Number of simple labeled graphs on n+4 nodes with exactly n connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215864/b215864.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: (7*x^3+59*x^2-34*x-137)*x/(x-1)^9.
%F a(n) = C(n+4,5)*(15*n^3+390*n^2+2285*n+3886)/48.
%p a:= n-> binomial(n+4,5)*(3886+(2285+(390+15*n)*n)*n)/48:
%p seq(a(n), n=0..40);
%t CoefficientList[Series[(7x^3+59x^2-34x-137)x/(x-1)^9,{x,0,30}],x] (* _Harvey P. Dale_, Jul 18 2019 *)
%Y A diagonal of A215861.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Aug 25 2012
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