%I A089436
%S A089436 1,2,9,54,374,2820,22485,186494,1592778,13914108,123750874,1116809628,
%T A089436 10201516332,94140605832,876332565837,8219124900558,77594375595266,
%U A089436 736785675010380,7031930543228910,67420537625021460,649070964647075700
%N A089436 Number of non-crossing connected graphs on n nodes on a circle in which 
               a fixed (distinguished) node has degree one.
%C A089436 Convolution of (1, A007297) with itself.
%D A089436 P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, 
               Discrete Math. 204 (1999), 203-229.
%F A089436 G.f.=g^2, where g satisfies g^3+g^2-3zg+2z^2=0, g(0)=0, or, in Maple 
               notation, g := -1/3+(2/3)*sqrt(1+9*z)*sin((1/3)*arcsin((2+27*z+54*z^2)/
               2/(1+9*z)^(3/2))).
%e A089436 a(3)=2 because among the four non-crossing graphs on the points A,B,C, 
               the distinguished node A has degree equal to 1 only in the graphs 
               {AB,BC} and {AC,BC}; in the other two graphs ({AB,AC} and {AB,BC,
               AC}) the node A has degree 2.
%Y A089436 Cf. A007297.
%Y A089436 Sequence in context: A080146 A074602 A073986 this_sequence A000168 A127128 
               A064151
%Y A089436 Adjacent sequences: A089433 A089434 A089435 this_sequence A089437 A089438 
               A089439
%K A089436 nonn
%O A089436 2,2
%A A089436 Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003