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 (terms n=23..100 from Vincenzo Librandi)
FORMULA
a(n) = A135313(n+1,n).
a(n) ~ n! * n^2 / (4 * log(2)^(n+2)). - 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+1, n): seq(a(n), n=0..20);
MATHEMATICA
t[k_] := t[k] = If[k < 0, 0&, Function[x, Evaluate @ Normal[Series[Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]], {x, 0, k+2}]]]]; tt[k_] := tt[k] = Function[x, (t[k][x]-t[k-1][x]) // Evaluate]; T[n_, k_] := T[n, k] = Coefficient[Series[tt[k][x], {x, 0, n+1}], x, n]*n!; a[n_] := a[n] = T[n+1, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 17 2014, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2012
STATUS
approved