A218105 Number of transitive reflexive early confluent binary relations R on n+5 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 11592, 1812216, 92374107, 3151808478, 94494907584, 2755081426548, 81009491387682, 2437976801668408, 75638497021149062, 2427804103875438288, 80751743315656443940, 2784897386029995089700, 99580133563729334883624, 3690405873805797826482120

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+5,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+5, n): seq(a(n), n=0..20);

Mathematica

m = 5; 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

Cf. A135313.

Sequence in context: A371390 A184685 A203387 * A226905 A162865 A237534

Adjacent sequences: A218102 A218103 A218104 * A218106 A218107 A218108

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2012

Status

approved