A317795 Number of non-isomorphic set-systems spanning n vertices with no singletons.

1, 0, 1, 6, 172, 611852, 200253853704512, 263735716028826427334553305221120, 5609038300883759793482640992086670066496449147691597380832361377955840

Offset: 0

Author

Gus Wiseman, Aug 07 2018

Keywords

• nonn

Examples

			Non-isomorphic representatives of the a(3) = 6 set-systems:
  {123}
  {12}{13}
  {12}{123}
  {12}{13}{23}
  {12}{13}{123}
  {12}{13}{23}{123}
		

Crossrefs

First differences of A317794.

Cf. A000088, A000612, A003180, A007716, A055621, A283877, A300913, A306005, A317533, A317757, A319876.

Programs

Mathematica

sysnorm[{}]:={};sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]],sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]],i},{i,Length[Union@@m]}]],First[Sort[sysnorm[m,1]]]];sysnorm[m_,aft_]:=If[Length[Union@@m]<=aft,{m},With[{mx=Table[Count[m,i,{2}],{i,Select[Union@@m,#>=aft&]}]},Union@@(sysnorm[#,aft+1]&/@Union[Table[Map[Sort,m/.{par+aft-1->aft,aft->par+aft-1},{0,1}],{par,First/@Position[mx,Max[mx]]}]])]];
Table[Length[Union[sysnorm/@Select[Subsets[Select[Subsets[Range[n]],Length[#]>1&]],Union@@#==Range[n]&]]],{n,4}]

Extensions

More terms from Gus Wiseman, Dec 13 2018