A210911 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 3 for all x.

1, 1, 4, 26, 168, 1416, 13897, 153126, 1893180, 25796852, 383636151, 6177688914, 106969864696, 1980478817526, 39015578535585, 814416108606566, 17947777613632128, 416233580676722424, 10129555365300697267, 258028441032419619786, 6864011282184757297896

Offset: 0

Author

Alois P. Heinz, Mar 29 2012

Keywords

• nonn

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..448

Crossrefs

Column k=3 of A135302.

Programs

Maple

gf:= exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6):
a:= n-> n!* coeff(series(gf,x,n+1), x, n):
seq(a(n), n=0..30);

Mathematica

t[0, ] = 1; t[k, x_] := t[k, x] = Exp[Sum[x^m/m!*t[k-m, x], {m, 1, k}]]; a[0, 0] = 1; a[, 0] = 0; a[n, k_] := SeriesCoefficient[t[k, x], {x, 0, n}]*n!; Table[a[n, 3], {n, 0, 30} ] (* Jean-François Alcover, Feb 04 2014, after A135302 and Alois P. Heinz *)

Formula

E.g.f.: exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6).