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A210913
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Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 5 for all x.
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4
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1, 1, 4, 26, 243, 2992, 41223, 660220, 11979669, 243048992, 5448497434, 133595966164, 3555887814602, 102064563003898, 3141580135645330, 103198691666336823, 3602725068242695657, 133174089439019869924, 5195463138498447345478, 213295995976349091757666
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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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REFERENCES
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A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
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LINKS
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FORMULA
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E.g.f.: t_5(x), where t_k(x) = exp (Sum_{m=1..k} x^m/m! * t_{k-m}(x)) for k>=0 and t_k(x) = 0 otherwise.
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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:
gf:= t(5)(x):
a:= n-> n!*coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);
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MATHEMATICA
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t[0, _] = 1; t[k_, x_] := t[k, x] = Exp[Sum[x^m/m!*t[k - m, x], {m, 1, k}]]; a[0, 0] = 1; a[_, 0] = 0; a[n_, k_] := SeriesCoefficient[t[k, x], {x, 0, n}]*n!; Table[a[n, 5], {n, 0, 30} ] (* Jean-François Alcover, Feb 04 2014, after A135302 and Alois P. Heinz *)
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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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