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A210915 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 7 for all x.

%I A210915 #15 Aug 02 2021 14:23:06
%S A210915 1,1,4,26,243,2992,45906,845287,17637091,412976516,10702355041,
%T A210915 304058582059,9396887340381,313853270626962,11265355519125229,
%U A210915 432420217726582213,17674492093095982705,766343475354260380416,35129831766609666284023,1697466558811335003294745
%N A210915 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 7 for all x.
%C A210915 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A210915 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A210915 Alois P. Heinz, <a href="/A210915/b210915.txt">Table of n, a(n) for n = 0..200</a>
%F A210915 E.g.f.: t_7(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 A210915 t:= proc(k) option remember;
%p A210915       `if`(k<0, 0, unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p A210915     end:
%p A210915 gf:= t(7)(x):
%p A210915 a:= n-> n!* coeff(series(gf, x, n+1), x, n):
%p A210915 seq(a(n), n=0..30);
%t A210915 t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]]; gf = t[7][x]; a[n_] := n!*SeriesCoefficient[gf, {x, 0, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 13 2014, translated from Maple *)
%Y A210915 Column k=7 of A135302.
%K A210915 nonn
%O A210915 0,3
%A A210915 _Alois P. Heinz_, Mar 29 2012