cp's OEIS Frontend

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

%I A317795 #8 Dec 13 2018 04:41:08
%S A317795 1,0,1,6,172,611852,200253853704512,263735716028826427334553305221120,
%T A317795 5609038300883759793482640992086670066496449147691597380832361377955840
%N A317795 Number of non-isomorphic set-systems spanning n vertices with no singletons.
%e A317795 Non-isomorphic representatives of the a(3) = 6 set-systems:
%e A317795   {123}
%e A317795   {12}{13}
%e A317795   {12}{123}
%e A317795   {12}{13}{23}
%e A317795   {12}{13}{123}
%e A317795   {12}{13}{23}{123}
%t A317795 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]]}]])]];
%t A317795 Table[Length[Union[sysnorm/@Select[Subsets[Select[Subsets[Range[n]],Length[#]>1&]],Union@@#==Range[n]&]]],{n,4}]
%Y A317795 First differences of A317794.
%Y A317795 Cf. A000088, A000612, A003180, A007716, A055621, A283877, A300913, A306005, A317533, A317757, A319876.
%K A317795 nonn
%O A317795 0,4
%A A317795 _Gus Wiseman_, Aug 07 2018
%E A317795 More terms from _Gus Wiseman_, Dec 13 2018