A210912 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 4 for all x.

1, 1, 4, 26, 243, 2451, 29922, 420841, 6692163, 118170959, 2296688956, 48661358989, 1115587992521, 27499790373121, 725031761113038, 20351018228318061, 605726610363853513, 19050158234570819809, 631097355371645795620, 21961423837720097681425

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..300

Formula

E.g.f.: exp(x *exp(x *exp(x *exp(x)+x^2/2) +x^2/2*exp(x) +x^3/6) +x^2/2 *exp(x*exp(x) +x^2/2) +x^3/6 *exp(x) +x^4/24).

Maple

gf:= exp(x *exp(x *exp(x *exp(x)+x^2/2) +x^2/2*exp(x) +x^3/6)
         +x^2/2 *exp(x*exp(x) +x^2/2) +x^3/6 *exp(x) +x^4/24):
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, 4], {n, 0, 30} ] (* Jean-François Alcover, Feb 04 2014, after A135302 and Alois P. Heinz *)

Crossrefs

Column k=4 of A135302.

Sequence in context: A302606 A052577 A203935 * A210913 A210914 A210915

Adjacent sequences: A210909 A210910 A210911 * A210913 A210914 A210915

Keyword

nonn

Author

Alois P. Heinz, Mar 29 2012

Status

approved