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A210918 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 10 for all x.

%I A210918 #15 Aug 02 2021 14:27:11
%S A210918 1,1,4,26,243,2992,45906,845287,18182926,447797646,12429760889,
%T A210918 382432412429,12895551865341,472172004983602,18636388954609376,
%U A210918 788226102638064075,35549770035085876130,1702625512220935301410,86287522467158470208030,4612838996164892567266399
%N A210918 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 10 for all x.
%C A210918 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A210918 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A210918 Alois P. Heinz, <a href="/A210918/b210918.txt">Table of n, a(n) for n = 0..200</a>
%F A210918 E.g.f.: t_10(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 A210918 t:= proc(k) option remember;
%p A210918       `if`(k<0, 0, unapply(exp(add(x^m/m!*t(k-m)(x), m=1..k)), x))
%p A210918     end:
%p A210918 gf:= t(10)(x):
%p A210918 a:= n-> n!*coeff(series(gf, x, n+1), x, n):
%p A210918 seq(a(n), n=0..30);
%t A210918 t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]]; gf = t[10][x]; a[n_] := n!*SeriesCoefficient[gf, {x, 0, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y A210918 Column k=10 of A135302.
%K A210918 nonn
%O A210918 0,3
%A A210918 _Alois P. Heinz_, Mar 29 2012