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%I #10 May 10 2020 04:28:41
%S 1,4,17,80,403,2128,11628,65208,373175,2170740,12797265,76292736,
%T 459162452,2786017120,17024247304,104673837384,647113502847,
%U 4020062732140
%N Maximum value in the distribution by first value of Prufer code of noncrossing spanning trees on a circle of n+2 points; perhaps the number whose Prufer code starts with 2.
%C Total in distribution is # t_n of ternary trees and one can prove first and last values in each distribution is t_{n-1}. Maximum appears to occur at 2, minimum near end; perhaps monotone between first, max, min, last. Distributions of Prufer code initial values, starting with 3 points: [1,1,1], [3,4,2,3], [12,17,9,5,12], [55,80,44,22,17,55], [273,403,227,112,68,72,273],[1428,2128,1218,603,335,267,345,1428].
%C First 200 values (n=3 to 202) of max occur at k=2; first 200 values of min (series A056098) occur at k=floor((n+5)/2).
%F G.f.: seems to be (g+1)/(1-g)^3 where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 10 2011
%e There are 12 noncrossing spanning trees on a circle of 4 points. The first values of their Prufer codes have distribution [3,4,2,3], e.g. 3 start with 1, 4 with 2 and so on. The maximum is a(4) = 4.
%Y Cf. A056098.
%K nonn,more
%O 3,2
%A David S. Hough (hough(AT)gwu.edu), Aug 04 2000
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