cp's OEIS Frontend

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

%I A261238 #25 Jun 27 2022 07:45:46
%S A261238 1,1,61,12075,4798983,3151808478,3085918099231,4210378306984993,
%T A261238 7631859877504516225,17735784941946000072572,
%U A261238 51404873131596488549863350,181773929944698613445522139632,770224297920086034338727292711511,3852558194920465350481058381000064850
%N A261238 Number of transitive reflexive early confluent binary relations R on 2n labeled elements where max_{x}(|{y:xRy}|)=n.
%C A261238 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%H A261238 Alois P. Heinz, <a href="/A261238/b261238.txt">Table of n, a(n) for n = 0..100</a>
%F A261238 a(n) = A135313(2n,n).
%F A261238 a(n) ~ c * d^n * n^(2*n), where d = 4.307069427308178... and c = 0.2607079596895... - _Vaclav Kotesovec_, Nov 20 2021
%p A261238 t:= proc(k) option remember; `if`(k<0, 0,
%p A261238        exp(add(x^m/m!*t(k-m), m=1..k)))
%p A261238     end:
%p A261238 A:= proc(n, k) option remember;
%p A261238       coeff(series(t(k), x, n+1), x, n) *n!
%p A261238     end:
%p A261238 a:= n-> A(2*n,n) -A(2*n,n-1):
%p A261238 seq(a(n), n=0..14);
%t A261238 t[k_] := t[k] = If[k < 0, 0, Exp[Sum[x^m/m!*t[k-m], {m, 1, k}]]];
%t A261238 A[n_, k_] := A[n, k] = SeriesCoefficient[t[k], {x, 0, n}]*n!;
%t A261238 a[n_] := A[2n, n] - A[2n, n-1];
%t A261238 Table[a[n], {n, 0, 14}] (* _Jean-François Alcover_, Jun 27 2022, after _Alois P. Heinz_ *)
%Y A261238 Cf. A135313.
%K A261238 nonn
%O A261238 0,3
%A A261238 _Alois P. Heinz_, Nov 18 2015