OFFSET
0,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
FORMULA
a(n) = n!*[x^n][y^n] exp(x)*(1 + log(Sum_{k>=0} (1 + y)^binomial(k, 2)*x^k/k!). - Andrew Howroyd, Feb 19 2024
EXAMPLE
The a(0) = 0 through a(4) = 15 graphs:
{} . . {{1,2},{1,3},{2,3}} {{1,2},{1,3},{1,4},{2,3}}
{{1,2},{1,3},{1,4},{2,4}}
{{1,2},{1,3},{1,4},{3,4}}
{{1,2},{1,3},{2,3},{2,4}}
{{1,2},{1,3},{2,3},{3,4}}
{{1,2},{1,3},{2,4},{3,4}}
{{1,2},{1,4},{2,3},{2,4}}
{{1,2},{1,4},{2,3},{3,4}}
{{1,2},{1,4},{2,4},{3,4}}
{{1,2},{2,3},{2,4},{3,4}}
{{1,3},{1,4},{2,3},{2,4}}
{{1,3},{1,4},{2,3},{3,4}}
{{1,3},{1,4},{2,4},{3,4}}
{{1,3},{2,3},{2,4},{3,4}}
{{1,4},{2,3},{2,4},{3,4}}
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[#]==n&&Length[csm[#]]<=1&]], {n, 0, 5}]
PROG
(PARI) a(n)=n!*polcoef(polcoef(exp(x + O(x*x^n))*(1 + 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 17 2024
EXTENSIONS
a(8) onwards from Andrew Howroyd, Feb 19 2024
STATUS
approved