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A218109
Number of transitive reflexive early confluent binary relations R on n+9 labeled elements with max_{x}(|{y : xRy}|) = n.
2
0, 1, 42159238, 106586385708, 25519311555595, 2416548374532292, 151442406160585540, 7894403946290257968, 379961855272982538127, 17735784941946000072572, 822369813313954835099742, 38353581871007817965010668, 1811813065380635747237663856
OFFSET
0,3
COMMENTS
R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
LINKS
FORMULA
a(n) = A135313(n+9,n).
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+9, n): seq(a(n), n=0..20);
MATHEMATICA
m = 9; f[0, _] = 1; f[k_, x_] := f[k, x] = Exp[Sum[x^m/m!*f[k-m, x], {m, 1, k}]]; (* t = A135302 *) t[0, 0] = 1; t[_, 0] = 0; t[n_, k_] := t[n, k] = SeriesCoefficient[f[k, x], {x, 0, n}]*n!; a[0] = 0; a[n_] := t[n+m, n]-t[n+m, n-1]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 14 2014 *)
CROSSREFS
Cf. A135313.
Sequence in context: A274812 A251306 A198168 * A263561 A213737 A254091
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2012
STATUS
approved