This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218109 #16 Aug 02 2021 08:40:05
%S A218109 0,1,42159238,106586385708,25519311555595,2416548374532292,
%T A218109 151442406160585540,7894403946290257968,379961855272982538127,
%U A218109 17735784941946000072572,822369813313954835099742,38353581871007817965010668,1811813065380635747237663856
%N A218109 Number of transitive reflexive early confluent binary relations R on n+9 labeled elements with max_{x}(|{y : xRy}|) = n.
%C A218109 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%H A218109 Alois P. Heinz, <a href="/A218109/b218109.txt">Table of n, a(n) for n = 0..200</a>
%F A218109 a(n) = A135313(n+9,n).
%p A218109 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:
%p A218109 a:= n-> T(n+9,n): seq(a(n), n=0..20);
%t A218109 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 *)
%Y A218109 Cf. A135313.
%K A218109 nonn
%O A218109 0,3
%A A218109 _Alois P. Heinz_, Oct 20 2012