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%I #13 Aug 02 2021 14:33:18
%S 545835,27733869,1173919350,47488375440,1933688266686,81009491387682,
%T 3527548086703069,160415345420268510,7631859877504516225,
%U 379961855272982538127,19785139747357478264082,1076480694153554931849504,61126131119735946242652270
%N Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 8.
%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="/A218098/b218098.txt">Table of n, a(n) for n = 8..200</a>
%F E.g.f.: t_8(x)-t_7(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) = A210916(n) - A210915(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(8)(x)-t(7)(x):
%p a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p seq(a(n), n=8..22);
%t m = 8; 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 Column k=8 of A135313.
%K nonn
%O 8,1
%A _Alois P. Heinz_, Oct 20 2012
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