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A122836
Number of topologies on n labeled elements in which at least one element belongs to some pair of noncomparable members of the topology.
2
0, 0, 0, 10, 243, 6131, 202503, 9464302, 641960602, 63249658532, 8976900501699, 1816843604787333, 519355528928422629, 207881392866381430470, 115617051961092253351796, 88736269118240819706018342, 93411113411702066083187522063, 134137950093337685116171325021995, 261492535743634369726764132015849219
OFFSET
0,4
COMMENTS
See comments in A122835.
REFERENCES
J. Munkres, Topology, Prentice Hall, (2000), p. 76.
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 *)
CROSSREFS
a(n) = A000798(n) - A122835(n).
Sequence in context: A064757 A087435 A331611 * A116878 A218307 A249564
KEYWORD
hard,nice,nonn
AUTHOR
Nathan K. McGregor (mcgregnk(AT)ese.wustl.edu), Sep 15 2006
EXTENSIONS
a(13) corrected and a(16)-a(18) by Jean-François Alcover, Jan 01 2020
STATUS
approved