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A218094 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 4.

%I A218094 #14 Aug 02 2021 07:50:53
%S A218094 75,1035,16025,267715,4798983,92374107,1913052805,42483670075,
%T A218094 1008618127825,25519311555595,686016182577453,19536602119711495,
%U A218094 587778832750221385,18633924653894097385,620967800006345098353,21703395396687678061639,793901738815689934686095
%N A218094 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 4.
%C A218094 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A218094 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A218094 Alois P. Heinz, <a href="/A218094/b218094.txt">Table of n, a(n) for n = 4..200</a>
%F A218094 E.g.f.: t_4(x)-t_3(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 A218094 a(n) = A210912(n) - A210911(n).
%p A218094 t:= proc(k) option remember; `if`(k<0, 0,
%p A218094       unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p A218094     end:
%p A218094 egf:= t(4)(x)-t(3)(x):
%p A218094 a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p A218094 seq(a(n), n=4..20);
%t A218094 m = 4; 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 A218094 Column k=4 of A135313.
%K A218094 nonn
%O A218094 4,1
%A A218094 _Alois P. Heinz_, Oct 20 2012