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A210914 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 6 for all x.

%I A210914 #16 Aug 02 2021 14:21:50
%S A210914 1,1,4,26,243,2992,45906,797994,15774047,348543878,8517326911,
%T A210914 228090873748,6641805913833,208882903017855,7054977212140236,
%U A210914 254641097826922363,9780088146805724737,398202474048334638184,17130262219179411169927,776303072938412423933278
%N A210914 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 6 for all x.
%C A210914 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A210914 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A210914 Alois P. Heinz, <a href="/A210914/b210914.txt">Table of n, a(n) for n = 0..200</a>
%F A210914 E.g.f.: t_6(x), where t_k(x) = exp (Sum_{m=1..k} x^m/m! * t_{k-m}(x)) for k>=0 and t_k(x) = 0 otherwise.
%p A210914 t:= proc(k) option remember;
%p A210914       `if`(k<0, 0, unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p A210914     end:
%p A210914 gf:= t(6)(x):
%p A210914 a:= n-> n!* coeff(series(gf, x, n+1), x, n):
%p A210914 seq(a(n), n=0..20);
%t A210914 t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]]; gf = t[6][x]; a[n_] := n!*SeriesCoefficient [gf, {x, 0, n}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 13 2014, translated from Maple *)
%Y A210914 Column k=6 of A135302.
%K A210914 nonn
%O A210914 0,3
%A A210914 _Alois P. Heinz_, Mar 29 2012