A218104 Number of transitive reflexive early confluent binary relations R on n+4 labeled elements with max_{x}(|{y : xRy}|) = n.

0, 1, 1821, 141533, 4798983, 124878033, 3068829477, 75967708311, 1933688266686, 51075201835515, 1405508547112670, 40356644902123914, 1209368372802130814, 37806870603888974350, 1231961629420423620918, 41802174277488971170242, 1475352032068521550599837

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+4,n).

a(n) ~ n! * n^8 / (768 * log(2)^(n+5)). - Vaclav Kotesovec, Nov 20 2021

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+4, n): seq(a(n), n=0..20);

Mathematica

m = 4; 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: A238030 A233719 A174770 * A171349 A256076 A179581

Adjacent sequences: A218101 A218102 A218103 * A218105 A218106 A218107

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2012

Status

approved