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 A210915 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 7 for all x. 4
 1, 1, 4, 26, 243, 2992, 45906, 845287, 17637091, 412976516, 10702355041, 304058582059, 9396887340381, 313853270626962, 11265355519125229, 432420217726582213, 17674492093095982705, 766343475354260380416, 35129831766609666284023, 1697466558811335003294745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z. REFERENCES A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA E.g.f.: t_7(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. MAPLE 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(7)(x): a:= n-> n!* coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..30); MATHEMATICA t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]]; gf = t[7][x]; a[n_] := n!*SeriesCoefficient[gf, {x, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 13 2014, translated from Maple *) CROSSREFS Column k=7 of A135302. Sequence in context: A210912 A210913 A210914 * A210916 A210917 A210918 Adjacent sequences: A210912 A210913 A210914 * A210916 A210917 A210918 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 29 2012 STATUS approved

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Last modified March 28 08:18 EDT 2023. Contains 361580 sequences. (Running on oeis4.)