%I A050168
%S A050168 1,2,3,5,9,16,30,55,105,196,378,714,1386,2640,5148,9867,19305,37180,
%T A050168 72930,140998,277134,537472,1058148,2057510,4056234,7904456,15600900,
%U A050168 30458900,60174900,117675360,232676280,455657715,901620585,1767883500
%N A050168 a(0) = 1; for n>0, a(n) = C(n, [n/2]) + C(n-1, [n/2]).
%C A050168 a(n) = number of symmetric Dyck (n+1)-paths which either start UD or 
               are prime i.e. do not return to ground level until the terminal point. 
               For example, a(2)=3 counts UUUDDD, UUDUDD, UDUDUD. - David Callan 
               (callan(AT)stat.wisc.edu), Dec 09 2004
%C A050168 a(n) = number of symmetric Dyck (n+1)-paths that first return to ground 
               level either right away or not until the very end, i.e., that remain 
               Dyck paths when either the first two steps or the first and last 
               steps are deleted. For example, a(2)=3 counts UUUDDD, UUDUDD, UDUDUD. 
               - David Callan (callan(AT)stat.wisc.edu), Mar 02 2005
%C A050168 Hankel transform has g.f. (1-x(1+x)^2)/(1-x^2(1-x^2)); - Paul Barry (pbarry(AT)wit.ie), 
               Sep 13 2007
%F A050168 Asymptotic to c*2^n/sqrt(n) where c=3/4*sqrt(2/Pi)=0.598413... - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Jan 13 2003
%Y A050168 Maximum element in n-th row of A029653 (generalized Pascal triangle).
%Y A050168 Sequence in context: A000050 A050253 A107250 this_sequence A072176 A047061 
               A136169
%Y A050168 Adjacent sequences: A050165 A050166 A050167 this_sequence A050169 A050170 
               A050171
%K A050168 nonn
%O A050168 0,2
%A A050168 Clark Kimberling (ck6(AT)evansville.edu)