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A050168
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a(0) = 1; for n>0, a(n) = C(n, [n/2]) + C(n-1, [n/2]).
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2
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1, 2, 3, 5, 9, 16, 30, 55, 105, 196, 378, 714, 1386, 2640, 5148, 9867, 19305, 37180, 72930, 140998, 277134, 537472, 1058148, 2057510, 4056234, 7904456, 15600900, 30458900, 60174900, 117675360, 232676280, 455657715, 901620585, 1767883500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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
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
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FORMULA
| 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
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CROSSREFS
| Maximum element in n-th row of A029653 (generalized Pascal triangle).
Sequence in context: A050253 A198518 A107250 * A072176 A047061 A136169
Adjacent sequences: A050165 A050166 A050167 * A050169 A050170 A050171
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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