|
|
A210918
|
|
Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 10 for all x.
|
|
3
|
|
|
1, 1, 4, 26, 243, 2992, 45906, 845287, 18182926, 447797646, 12429760889, 382432412429, 12895551865341, 472172004983602, 18636388954609376, 788226102638064075, 35549770035085876130, 1702625512220935301410, 86287522467158470208030, 4612838996164892567266399
(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
|
|
|
FORMULA
|
E.g.f.: t_10(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(10)(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[10][x]; a[n_] := n!*SeriesCoefficient[gf, {x, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 13 2014, after Maple *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|