A210917 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 9 for all x.

1, 1, 4, 26, 243, 2992, 45906, 845287, 18182926, 447797646, 12327513326, 374460094229, 12417692352452, 445937963850159, 17230880407496706, 712587605616915013, 31399448829720502520, 1468521294946336416768, 72650756455913144620677, 3790469182850937732166657

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_9(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(9)(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[9][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=9 of A135302.

Sequence in context: A210914 A210915 A210916 * A210918 A052880 A090357

Adjacent sequences: A210914 A210915 A210916 * A210918 A210919 A210920

Keyword

nonn

Author

Alois P. Heinz, Mar 29 2012

Status

approved