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A261238 Number of transitive reflexive early confluent binary relations R on 2n labeled elements where max_{x}(|{y:xRy}|)=n. 2
1, 1, 61, 12075, 4798983, 3151808478, 3085918099231, 4210378306984993, 7631859877504516225, 17735784941946000072572, 51404873131596488549863350, 181773929944698613445522139632, 770224297920086034338727292711511, 3852558194920465350481058381000064850 (list; graph; refs; listen; history; text; internal format)
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..100

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

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-Fran├žois Alcover, Jun 27 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A135313.

Sequence in context: A090823 A093261 A062638 * A197105 A195216 A259412

Adjacent sequences:  A261235 A261236 A261237 * A261239 A261240 A261241

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 18 2015

STATUS

approved

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Last modified September 27 06:29 EDT 2022. Contains 357052 sequences. (Running on oeis4.)