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-François Alcover, Jun 27 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 18 2015
STATUS
approved