A218109 Number of transitive reflexive early confluent binary relations R on n+9 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 42159238, 106586385708, 25519311555595, 2416548374532292, 151442406160585540, 7894403946290257968, 379961855272982538127, 17735784941946000072572, 822369813313954835099742, 38353581871007817965010668, 1811813065380635747237663856

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

Crossrefs

Cf. A135313.

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+9,n): seq(a(n), n=0..20);

Mathematica

m = 9; 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+9,n).