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A326878
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Number of topologies whose points are a subset of {1..n}.
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23
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1, 2, 7, 45, 500, 9053, 257151, 11161244, 725343385, 69407094565, 9639771895398, 1919182252611715, 541764452276876719, 214777343584048313318, 118575323291814379721651, 90492591258634595795504697, 94844885130660856889237907260, 135738086271526574073701454370969, 263921383510041055422284977248713291
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(x)*A(exp(x)-1) where A(x) is the e.g.f. for A001035.
a(n) = Sum_{k=0..n} binomial(n,k)*A000798(k). (End)
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EXAMPLE
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The a(0) = 1 through a(2) = 7 topologies:
{{}} {{}} {{}}
{{},{1}} {{},{1}}
{{},{2}}
{{},{1,2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{},{1},{2},{1,2}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n]]], MemberQ[#, {}]&&SubsetQ[#, Union[Union@@@Tuples[#, 2], Intersection@@@Tuples[#, 2]]]&]], {n, 0, 4}]
(* Second program: *)
A000798 = Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {_, _}][[All, 2]];
a[n_] := Sum[Binomial[n, k]*A000798[[k+1]], {k, 0, n}];
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CROSSREFS
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Binomial transform of A000798 (the covering case).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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