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A215865 Number of simple labeled graphs on n+5 nodes with exactly n connected components that are trees or cycles.

%I A215865 #7 Dec 04 2014 07:11:37
%S A215865 0,1356,15029,90734,394506,1381695,4138827,11002068,26603148,59546487,
%T A215865 124984860,248436188,471271892,858408642,1508851218,2569865520,
%U A215865 4255708464,6872006526,10847057991,16771536474,25448295950,37954221305,55716334245,80604653220
%N A215865 Number of simple labeled graphs on n+5 nodes with exactly n connected components that are trees or cycles.
%H A215865 Alois P. Heinz, <a href="/A215865/b215865.txt">Table of n, a(n) for n = 0..1000</a>
%F A215865 G.f.: (194*x^4-713*x^3-5*x^2+113*x+1356)*x/(1-x)^11.
%F A215865 a(n) = C(n+5,6)*(3*n^4+130*n^3+1565*n^2+7006*n+12992)/16.
%p A215865 a:= n-> binomial(n+5,6)*(12992+(7006+(1565+(130+3*n)*n)*n)*n)/16:
%p A215865 seq(a(n), n=0..40);
%Y A215865 A diagonal of A215861.
%K A215865 nonn
%O A215865 0,2
%A A215865 _Alois P. Heinz_, Aug 25 2012