A218108 Number of transitive reflexive early confluent binary relations R on n+8 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 4910785, 6135529675, 1008618127825, 74564772630777, 3913397076494906, 177779119899659850, 7631859877504516225, 322215964319093498225, 13636766011245325587353, 584294217357391235758011, 25488316708898114509899955, 1135731969645865474902932115

Offset: 0

Author

Alois P. Heinz, Oct 20 2012

Keywords

• nonn

Comments

R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Programs

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: tt:= proc(k) option remember; unapply ((t(k)-t(k-1))(x), x) end: T:= proc(n, k) option remember; coeff (series (tt(k)(x), x, n+1), x, n) *n! end:
a:= n-> T(n+8,n): seq (a(n), n=0..20);

Mathematica

m = 8; f[0, ] = 1; f[k, x_] := f[k, x] = Exp[Sum[x^m/m!*f[k-m, x], {m, 1, k}]]; (* t = A135302 *) t[0, 0] = 1; t[, 0] = 0; t[n, k_] := t[n, k] = SeriesCoefficient[f[k, x], {x, 0, n}]*n!; a[0] = 0; a[n_] := t[n+m, n]-t[n+m, n-1]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 14 2014 *)

Formula

a(n) = A135313(n+8,n).