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_6(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(6)(x):
a:= n-> n!* coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);
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[6][x]; a[n_] := n!*SeriesCoefficient [gf, {x, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 13 2014, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 29 2012
STATUS
approved