A182166 The total number of components of size 2 over all simple labeled graphs on n nodes.

1, 3, 12, 80, 960, 21504, 917504, 75497472, 12079595520, 3779571220480, 2322168557862912, 2810246167479189504, 6714614842830276788224, 31734302764884015836037120, 297105609428491265975789813760, 5516815412193254355313652349796352

Offset: 2

Author

Geoffrey Critzer, Apr 15 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..50

Crossrefs

Cf. A000217, A006125.

Programs

Magma

B:=Binomial; [B(n,2)*2^B(n-2,2): n in [2..20]]; // G. C. Greubel, Sep 04 2022

Maple

a:= n-> binomial(n, 2) *2^binomial(n-2, 2):
seq (a(n), n=2..20);  # Alois P. Heinz, Apr 16 2012

Mathematica

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]

SageMath

b=binomial; [b(n,2)*2^b(n-2,2) for n in (2..20)] # G. C. Greubel, Sep 04 2022

Formula

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

a(n) = C(n,2) * 2^C(n-2,2). - Alois P. Heinz, Apr 16 2012