OFFSET
0,5
COMMENTS
The case of an empty edge set is excluded.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
FORMULA
Binomial transform of A057500 (if the null graph is not connected).
a(n) = n!*[x^n][y^n] exp(x*y)*(-x + log(Sum_{k>=0} (1 + y)^binomial(k, 2)*x^k/k!). - Andrew Howroyd, Feb 19 2024
MATHEMATICA
csm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], Length[Intersection@@s[[#]]]>0&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[#]==Length[Union@@#] && Length[csm[#]]==1&]], {n, 0, 5}]
PROG
a(n)=n!*polcoef(polcoef(exp(x*y + O(x*x^n))*(-x+log(sum(k=0, n, (1 + y + O(y*y^n))^binomial(k, 2)*x^k/k!, O(x*x^n)))), n), n) \\ Andrew Howroyd, Feb 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 18 2024
STATUS
approved