A218110 Number of transitive reflexive early confluent binary relations R on n+10 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 383478987, 1976799958367, 686016182577453, 82847673438018762, 6177363078563029080, 368141001305925742232, 19785139747357478264082, 1016521929886047797022408, 51404873131596488549863350, 2597923441011463423121994276, 132340384137811145863910654038

Offset

0,3

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

Formula

a(n) = A135313(n+10,n).

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+10, n): seq (a(n), n=0..20);

Mathematica

m = 10; 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 *)

Crossrefs

Sequence in context: A257954 A218455 A297848 * A233485 A057071 A074152

Adjacent sequences: A218107 A218108 A218109 * A218111 A218112 A218113

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2012

Status

approved