%I A036771
%S A036771 1,4,420,201600,264264000,734557824000,3723191087616000,31125877492469760000,
%T A036771 399532678960326912000000,7462849882264211635200000000,194563959280510261541299200000000,
%U A036771 6847568575944052279580806348800000000
%N A036771 Number of labeled rooted trees with a degree constraint: (3*n)!/(6^n))*binomial(3*n+1,
               n).
%D A036771 L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 
               (1993), 1-10, esp. Eq. (12).
%H A036771 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A036771 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=47">
               Encyclopedia of Combinatorial Structures 47</a>
%F A036771 E.g.f.: -(1/2)/x*((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3)-1/((-3*x+((-8+9*x^3)/
               x)^(1/2))*x^2)^(1/3)-1/2*I*3^(1/2)*(1/x*((-3*x+((-8+9*x^3)/x)^(1/
               2))*x^2)^(1/3)-2/((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3))
%F A036771 Recurrence: {a(0)=0, a(2)=0, (-9*n^4-45*n^3-63*n^2-27*n)*a(n)+(8*n+28)*a(n+3)}
%p A036771 spec := [S,{S=Union(Z,Prod(Z,Set(S,card=3)))},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%Y A036771 Cf. A036770.
%Y A036771 Sequence in context: A116031 A115049 A158111 this_sequence A080321 A125760 
               A053780
%Y A036771 Adjacent sequences: A036768 A036769 A036770 this_sequence A036772 A036773 
               A036774
%K A036771 nonn
%O A036771 0,2
%A A036771 N. J. A. Sloane (njas(AT)research.att.com).