%I A100299
%S A100299 0,2,5,23,98,452,2139,10397,51524,259430,1323361,6824435,35519686,
%T A100299 186346760,984400759,5231789177,27954506504,150079713482,809181079293,
%U A100299 4379654830223,23787413800490,129607968854732,708230837732435
%N A100299 Number of dissections of a convex n-gon by nonintersecting diagonals 
               into an even number of regions.
%D A100299 P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, 
               Discrete Math., 204, 1999, 203-229.
%F A100299 a(n)=sum(binom(n-3, 2k-1)*binom(n+2k-2, 2k-1)/(2k), k=1..floor((n-2)/
               2)). G.f.=(1/2)z^2/(1+z)+z/8-7z^2/8-(1/8)z*sqrt(1-6*z+z^2).
%e A100299 a(5)=5 because for a convex pentagon ABCDE we obtain dissections with 
               an even number of regions by one of the following sets of diagonals: 
               {AC}, {BD}, {CE}, {DA} and {EB}.
%p A100299 a:=n->sum(binomial(n-3,2*k-1)*binomial(n+2*k-2,2*k-1)/2/k,k=1..floor((n-2)/
               2)): seq(a(n),n=3..33);
%Y A100299 Cf. A100300.
%Y A100299 Sequence in context: A023186 A023188 A106858 this_sequence A038833 A003501 
               A006990
%Y A100299 Adjacent sequences: A100296 A100297 A100298 this_sequence A100300 A100301 
               A100302
%K A100299 nonn
%O A100299 3,2
%A A100299 Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 12 2004