A218107 Number of transitive reflexive early confluent binary relations R on n+7 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 608832, 378725365, 42483670075, 2440299822081, 106818340013957, 4210378306984993, 160415345420268510, 6093096859120003590, 234104217274598884642, 9167943015777908270142, 367520396335132750893274, 15117877192137817244318510, 638973577773301815522889410

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+7,n): seq (a(n), n=0..20);

Mathematica

m = 7; 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+7,n).