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%I #15 Aug 02 2021 14:30:39
%S 4683,137774,3794378,105494886,3068829477,94494907584,3085918099231,
%T 106818340013957,3913397076494906,151442406160585540,
%U 6177363078563029080,265028384609314768260,11934799080680963824449,563007076962063332175612,27770258520873025001499693
%N Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 6.
%C R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H Alois P. Heinz, <a href="/A218096/b218096.txt">Table of n, a(n) for n = 6..200</a>
%F E.g.f.: t_6(x)-t_5(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 a(n) = A210914(n) - A210913(n).
%p t:= proc(k) option remember; `if`(k<0, 0,
%p unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p end:
%p egf:= t(6)(x)-t(5)(x):
%p a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p seq(a(n), n=6..20);
%t m = 6; 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, 20}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y Column k=6 of A135313.
%K nonn
%O 6,1
%A _Alois P. Heinz_, Oct 20 2012
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