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A218097 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 7.

%I A218097 #13 Aug 02 2021 14:32:04
%S A218097 47293,1863044,64432638,2185028130,75967708311,2755081426548,
%T A218097 104970367609107,4210378306984993,177779119899659850,
%U A218097 7894403946290257968,368141001305925742232,17999569547430255114096,921163485872922579361467,49262708358493465135411860
%N A218097 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 7.
%C A218097 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A218097 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A218097 Alois P. Heinz, <a href="/A218097/b218097.txt">Table of n, a(n) for n = 7..200</a>
%F A218097 E.g.f.: t_7(x)-t_6(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 A218097 a(n) = A210915(n) - A210914(n).
%p A218097 t:= proc(k) option remember; `if`(k<0, 0,
%p A218097       unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p A218097     end:
%p A218097 egf:= t(7)(x)-t(6)(x):
%p A218097 a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p A218097 seq(a(n), n=7..22);
%t A218097 m = 7; 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 A218097 Column k=7 of A135313.
%K A218097 nonn
%O A218097 7,1
%A A218097 _Alois P. Heinz_, Oct 20 2012