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A369799
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Number of binary relations R on [n] such that q(R) is a quasi-order and s(R) is a strict partial order (where q(R) and s(R) are defined below).
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2
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1, 2, 13, 237, 11590, 1431913, 424559959, 292150780260, 456213083587511, 1589279411184268465, 12188163803127032036308, 203538148644721100472292979, 7336995548182992341725851094195, 566597426371900580541745092349604750, 93154354372753215966288131247384428212545, 32423220989898980232206367503220063835343283713
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OFFSET
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0,2
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COMMENTS
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For a relation R on [n], let E = domain(R intersect R^(-1)) and let F = [n]\E. Then q(R) := R intersect E X E and let s(R) := R intersect F X F.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A369776(n,k) * 3^(k*(n-k)).
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MATHEMATICA
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nn = 18; posets =Select[Import["https://oeis.org/A001035/b001035.txt", "Table"],
Length@# == 2 &][[All, 2]]; p[x_] := Total[posets Table[x^i/i!, {i, 0, 18}]]; Map[Total, (Map[Select[#, # > 0 &] &, Table[n!, {n, 0, nn}] CoefficientList[
Series[ p[Exp[ y x] - 1]*p[ x], {x, 0, nn}], {x, y}]])*
Table[Table[3^(k (n - k)), {k, 0, n}], {n, 0, nn}]]
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CROSSREFS
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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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