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%I #8 Dec 04 2014 07:04:01
%S 0,19,135,540,1610,3990,8694,17220,31680,54945,90805,144144,221130,
%T 329420,478380,679320,945744,1293615,1741635,2311540,3028410,3920994,
%U 5022050,6368700,8002800,9971325,12326769,15127560,18438490,22331160,26884440,32184944,38327520
%N Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215863/b215863.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (6*x^2-2*x-19)*x/(x-1)^7.
%F a(n) = C(n+3,4)*(n^2+13*n+24)/2.
%e a(1) = 19:
%e .1-2. .1-2. .1 2. .1-2. .1-2. .1 2. .1 2. .1 2. .1-2. .1-2.
%e .| |. . X . .|X|. .|\ . . /|. . \|. .|/ . .| |. .| . .| |.
%e .4-3. .4-3. .4.3. .4.3. .4.3. .4-3. .4-3. .4-3. .4-3. .4.3.
%e .
%e .1-2. .1 2. .1-2. .1-2. .1-2. .1 2. .1 2. .1 2. .1 2.
%e . |. . X . . / . . \ . . X . .|/|. . X|. .|X . .|\|.
%e .4-3. .4-3. .4-3. .4-3. .4.3. .4.3. .4.3. .4.3. .4.3.
%p a:= n-> binomial(n+3,4)*(24+(13+n)*n)/2:
%p seq(a(n), n=0..40);
%Y A diagonal of A215861.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 25 2012
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