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A210916
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Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 8 for all x.
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4
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1, 1, 4, 26, 243, 2992, 45906, 845287, 18182926, 440710385, 11876274391, 351546957499, 11330575607067, 394862762014644, 14792903605828298, 592835563146850723, 25306351970600498930, 1146305330627242918543, 54914971513967144548105, 2773947252964889935144249
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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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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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E.g.f.: t_8(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(8)(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[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]]; gf = t[8][x]; a[n_] := n!*SeriesCoefficient[gf, {x, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 13 2014, translated from Maple *)
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CROSSREFS
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Column k=8 of A135302.
Sequence in context: A210913 A210914 A210915 * A210917 A210918 A052880
Adjacent sequences: A210913 A210914 A210915 * A210917 A210918 A210919
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Mar 29 2012
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STATUS
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approved
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