OFFSET
0,4
COMMENTS
Graphs consist of zero or more paths on two nodes each and either a single isolated node or a star with two or more peripheral nodes. - Andrew Howroyd, Sep 05 2019
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
FORMULA
E.g.f.: x*exp(x^2/2)*(exp(x) - x). - Andrew Howroyd, Sep 05 2019
(n-1)*(n-2)*a(n) - n*(n-3)*(n-2)*a(n-1) - n*(n-1)^2*a(n-2) + (2*n-7)*n*(n-1)*(n-2)*a(n-3) - n*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) = 0. - Robert Israel, Sep 06 2019
EXAMPLE
The a(4) = 4 edge-sets:
{12,13,14}
{12,23,24}
{13,23,34}
{14,24,34}
MAPLE
f:= gfun:-rectoproc({(n-1)*(n-2)*a(n)-n*(n-3)*(n-2)*a(n-1)-n*(n-1)^2*a(n-2)+(2*n-7)*n*(n-1)*(n-2)*a(n-3)-n*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5)=0, a(0)=0, a(1)=1, a(2)=0, a(3)=6, a(4)=4}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Sep 06 2019
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Count[Length/@Split[Sort[Join@@#]], 1]==n-1&]], {n, 0, 5}]
With[{nn=30}, CoefficientList[Series[x Exp[x^2/2](Exp[x]-x), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Apr 28 2022 *)
PROG
(PARI) seq(n)={Vec(serlaplace(x*exp(x^2/2 + O(x^n))*(exp(x + O(x^n))-x)), -(n+1))} \\ Andrew Howroyd, Sep 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Sep 05 2019
STATUS
approved