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A317795 Number of non-isomorphic set-systems spanning n vertices with no singletons. 11
1, 0, 1, 6, 172, 611852, 200253853704512, 263735716028826427334553305221120, 5609038300883759793482640992086670066496449147691597380832361377955840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

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}

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}]

CROSSREFS

First differences of A317794.

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

Sequence in context: A266852 A266311 A323820 * A166762 A323279 A214801

Adjacent sequences:  A317792 A317793 A317794 * A317796 A317797 A317798

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 07 2018

EXTENSIONS

More terms from Gus Wiseman, Dec 13 2018

STATUS

approved

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Last modified August 11 10:15 EDT 2022. Contains 356065 sequences. (Running on oeis4.)