OFFSET
0,4
COMMENTS
Some graph theory texts call these graphs Eulerian. Cf. A033678.
REFERENCES
D. B. West, Introduction to Graph Theory, 2nd edition, Pearson Education, 2001, page 27.
FORMULA
E.g.f.: exp(x)*(log(A(x) + 1) - x + 1) where A(x) = Sum_{n>=1} 2^binomial(n-1,2)x^n/n!.
EXAMPLE
a(4) = 8 because there are 1+4+3=8 labelings on these three graphs
1)
o o
o o
2)
o-o
|/
o o
3)
o-o
| |
o-o
MATHEMATICA
nn = 18; Clear[g]; g[z_] := Sum[2^Binomial[n - 1, 2] z^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[Exp[z] (Log[g[z] + 1] - z + 1), {z, 0, nn}], z]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 28 2016
STATUS
approved