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A210914
Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 6 for all x.
4
1, 1, 4, 26, 243, 2992, 45906, 797994, 15774047, 348543878, 8517326911, 228090873748, 6641805913833, 208882903017855, 7054977212140236, 254641097826922363, 9780088146805724737, 398202474048334638184, 17130262219179411169927, 776303072938412423933278
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
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
Column k=6 of A135302.
Sequence in context: A203935 A210912 A210913 * A210915 A210916 A210917
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 29 2012
STATUS
approved