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A218111
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Number of transitive reflexive early confluent binary relations R on n+1 labeled elements with max_{x}(|{y : xRy}|) = n.
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2
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0, 1, 12, 106, 1035, 11301, 137774, 1863044, 27733869, 451238935, 7972318200, 152065270974, 3115418734415, 68245059703289, 1591993733475570, 39406010771574856, 1031649940977825633, 28483179899706237483, 827159099070697636124, 25205610503231757308450
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OFFSET
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0,3
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COMMENTS
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R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
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LINKS
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FORMULA
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MAPLE
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t:= proc(k) option remember; `if`(k<0, 0, unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x)) end: tt:= proc(k) option remember; unapply((t(k)-t(k-1))(x), x) end: T:= proc(n, k) option remember; coeff(series(tt(k)(x), x, n+1), x, n) *n! end:
a:= n-> T(n+1, n): seq(a(n), n=0..20);
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MATHEMATICA
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t[k_] := t[k] = If[k < 0, 0&, Function[x, Evaluate @ Normal[Series[Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]], {x, 0, k+2}]]]]; tt[k_] := tt[k] = Function[x, (t[k][x]-t[k-1][x]) // Evaluate]; T[n_, k_] := T[n, k] = Coefficient[Series[tt[k][x], {x, 0, n+1}], x, n]*n!; a[n_] := a[n] = T[n+1, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 17 2014, after Maple *)
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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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