A122836 Number of topologies on n labeled elements in which at least one element belongs to some pair of noncomparable members of the topology.

0, 0, 0, 10, 243, 6131, 202503, 9464302, 641960602, 63249658532, 8976900501699, 1816843604787333, 519355528928422629, 207881392866381430470, 115617051961092253351796, 88736269118240819706018342, 93411113411702066083187522063, 134137950093337685116171325021995, 261492535743634369726764132015849219

Offset: 0

Author

Nathan K. McGregor (mcgregnk(AT)ese.wustl.edu), Sep 15 2006

Keywords

• hard
• nice
• nonn

Comments

See comments in A122835.

References

• J. Munkres, Topology, Prentice Hall, (2000), p. 76.

Crossrefs

a(n) = A000798(n) - A122835(n).

Programs

Mathematica

A000798 = Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {, }][[All, 2]];
a122835[n_] := (3/4)*(PolyLog[-n, 1/2] + Boole[n == 0]) - 1/2;
a[n_] := A000798[[n + 1]] - a122835[n];
a /@ Range[0, 18] (* Jean-François Alcover, Jan 01 2020, after Michael Somos in A122835 *)

Extensions

a(13) corrected and a(16)-a(18) by Jean-François Alcover, Jan 01 2020