A261238 Number of transitive reflexive early confluent binary relations R on 2n labeled elements where max_{x}(|{y:xRy}|)=n.

1, 1, 61, 12075, 4798983, 3151808478, 3085918099231, 4210378306984993, 7631859877504516225, 17735784941946000072572, 51404873131596488549863350, 181773929944698613445522139632, 770224297920086034338727292711511, 3852558194920465350481058381000064850

Offset: 0

Author

Alois P. Heinz, Nov 18 2015

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..100

Crossrefs

Cf. A135313.

Programs

Maple

t:= proc(k) option remember; `if`(k<0, 0,
       exp(add(x^m/m!*t(k-m), m=1..k)))
    end:
A:= proc(n, k) option remember;
      coeff(series(t(k), x, n+1), x, n) *n!
    end:
a:= n-> A(2*n,n) -A(2*n,n-1):
seq(a(n), n=0..14);

Mathematica

t[k_] := t[k] = If[k < 0, 0, Exp[Sum[x^m/m!*t[k-m], {m, 1, k}]]];
A[n_, k_] := A[n, k] = SeriesCoefficient[t[k], {x, 0, n}]*n!;
a[n_] := A[2n, n] - A[2n, n-1];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

Formula

a(n) = A135313(2n,n).

a(n) ~ c * d^n * n^(2*n), where d = 4.307069427308178... and c = 0.2607079596895... - Vaclav Kotesovec, Nov 20 2021