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A218099 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 9.

%I A218099 #13 Aug 02 2021 14:34:39
%S A218099 7087261,451238935,22913136730,1087116745385,51075201835515,
%T A218099 2437976801668408,119752042470064290,6093096859120003590,
%U A218099 322215964319093498225,17735784941946000072572,1016521929886047797022408,60650840653136697085038930,3764766650086543657134295955
%N A218099 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 9.
%C A218099 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A218099 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A218099 Alois P. Heinz, <a href="/A218099/b218099.txt">Table of n, a(n) for n = 9..200</a>
%F A218099 E.g.f.: t_9(x)-t_8(x), with t_k(x) = exp (Sum_{m=1..k} x^m/m! * t_{k-m}(x)) if k>=0 and t_k(x) = 0 else.
%F A218099 a(n) = A210917(n) - A210916(n).
%p A218099 t:= proc(k) option remember; `if`(k<0, 0,
%p A218099       unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p A218099     end:
%p A218099 egf:= t(9)(x)-t(8)(x):
%p A218099 a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p A218099 seq(a(n), n=9..22);
%t A218099 m = 9; t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]] ; egf = t[m][x]-t[m-1][x]; a[n_] := n!*Coefficient[Series[egf, {x, 0, n+1}], x, n]; Table[a[n], {n, m, 22}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y A218099 Column k=9 of A135313.
%K A218099 nonn
%O A218099 9,1
%A A218099 _Alois P. Heinz_, Oct 20 2012