Search: id:A135307
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%I A135307
%S A135307 1,1,2,4,9,23,63,178,514,1515,4545,13827,42540,132124,413741,1304891,
%T A135307 4141198,13214815,42375461,136478383,441285890,1431925180,4661485203,
%U A135307 15219836738,49827678840,163535624722,537962562453,1773437280323
%N A135307 Number of Dyck paths of semilength n that do not contain the string UDDU.
%D A135307 A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck 
               paths, Discrete Math., 307 (2007), 2909-2924.
%F A135307 The Sapounakis et al. reference gives an explicit formula.
%p A135307 A135306 := proc(n,k) if n =0 then 1 ; else add((-1)^(j-k)*binomial(n-k,
               j-k)*binomial(2*n-3*j,n-j+1),j=k..floor((n-1)/2)) ; %*binomial(n,
               k)/n ; fi ; end: A135307 := proc(n) A135306(n,0) ; end: for n from 
               0 to 30 do printf("%a, ",A135307(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 08 2007
%Y A135307 Leading column of A135306.
%Y A135307 Sequence in context: A127384 A058585 A001573 this_sequence A000083 A092668 
               A164039
%Y A135307 Adjacent sequences: A135304 A135305 A135306 this_sequence A135308 A135309 
               A135310
%K A135307 nonn,easy
%O A135307 0,3
%A A135307 N. J. A. Sloane (njas(AT)research.att.com), Dec 07 2007
%E A135307 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2007

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