OFFSET
0,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
Binomial transform of A327362.
EXAMPLE
The a(4) = 46 edge-sets:
{12} {12,13} {12,13,14} {12,13,14,23}
{13} {12,14} {12,13,24} {12,13,14,24}
{14} {12,23} {12,13,34} {12,13,14,34}
{23} {12,24} {12,14,23} {12,13,23,24}
{24} {13,14} {12,14,34} {12,13,23,34}
{34} {13,23} {12,23,24} {12,14,23,24}
{13,34} {12,23,34} {12,14,24,34}
{14,24} {12,24,34} {12,23,24,34}
{14,34} {13,14,23} {13,14,23,34}
{23,24} {13,14,24} {13,14,24,34}
{23,34} {13,23,24} {13,23,24,34}
{24,34} {13,23,34} {14,23,24,34}
{13,24,34}
{14,23,24}
{14,23,34}
{14,24,34}
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[csm[#]]==1&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 5}]
PROG
(PARI) seq(n)={my(x=x + O(x*x^n)); Vec(serlaplace(exp(x)*(-x^2/2 + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k!)) - log(sum(k=0, n, 2^binomial(k, 2)*(x*exp(-x))^k/k!)))), -(n+1))} \\ Andrew Howroyd, Sep 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Sep 11 2019
STATUS
approved