A182166 - OEIS

%I #22 Sep 05 2022 05:25:25

%S 1,3,12,80,960,21504,917504,75497472,12079595520,3779571220480,

%T 2322168557862912,2810246167479189504,6714614842830276788224,

%U 31734302764884015836037120,297105609428491265975789813760,5516815412193254355313652349796352

%N The total number of components of size 2 over all simple labeled graphs on n nodes.

%H Alois P. Heinz, <a href="/A182166/b182166.txt">Table of n, a(n) for n = 2..50</a>

%F E.g.f.: x^2/2 * G(x) where G(x) is e.g.f. for A006125.

%F a(n) = C(n,2) * 2^C(n-2,2). - _Alois P. Heinz_, Apr 16 2012

%p a:= n-> binomial(n, 2) *2^binomial(n-2, 2):

%p seq (a(n), n=2..20);  # _Alois P. Heinz_, Apr 16 2012

%t nn = 20; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]! CoefficientList[Series[x^2/2 g, {x, 0, nn}], x], 2]

%o (Magma) B:=Binomial; [B(n,2)*2^B(n-2,2): n in [2..20]]; // _G. C. Greubel_, Sep 04 2022

%o (SageMath) b=binomial; [b(n,2)*2^b(n-2,2) for n in (2..20)] # _G. C. Greubel_, Sep 04 2022

%Y Cf. A000217, A006125.

%K nonn

%O 2,2

%A _Geoffrey Critzer_, Apr 15 2012