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A210912 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 4 for all x.

%I A210912 #16 Dec 04 2015 11:01:33
%S A210912 1,1,4,26,243,2451,29922,420841,6692163,118170959,2296688956,
%T A210912 48661358989,1115587992521,27499790373121,725031761113038,
%U A210912 20351018228318061,605726610363853513,19050158234570819809,631097355371645795620,21961423837720097681425
%N A210912 Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 4 for all x.
%C A210912 R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A210912 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A210912 Alois P. Heinz, <a href="/A210912/b210912.txt">Table of n, a(n) for n = 0..300</a>
%F A210912 E.g.f.: exp(x *exp(x *exp(x *exp(x)+x^2/2) +x^2/2*exp(x) +x^3/6) +x^2/2 *exp(x*exp(x) +x^2/2) +x^3/6 *exp(x) +x^4/24).
%p A210912 gf:= exp(x *exp(x *exp(x *exp(x)+x^2/2) +x^2/2*exp(x) +x^3/6)
%p A210912          +x^2/2 *exp(x*exp(x) +x^2/2) +x^3/6 *exp(x) +x^4/24):
%p A210912 a:= n-> n!* coeff(series(gf, x, n+1), x, n):
%p A210912 seq(a(n), n=0..30);
%t A210912 t[0, _] = 1; t[k_, x_] := t[k, x] = Exp[Sum[x^m/m!*t[k - m, x], {m, 1, k}]]; a[0, 0] = 1; a[_, 0] = 0; a[n_, k_] := SeriesCoefficient[t[k, x], {x, 0, n}]*n!; Table[a[n, 4], {n, 0, 30} ] (* _Jean-François Alcover_, Feb 04 2014, after A135302 and _Alois P. Heinz_ *)
%Y A210912 Column k=4 of A135302.
%K A210912 nonn
%O A210912 0,3
%A A210912 _Alois P. Heinz_, Mar 29 2012