Search: id:A128743
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%I A128743
%S A128743 0,0,2,13,69,346,1700,8286,40264,195488,949302,4613025,22436997,
%T A128743 109240038,532410060,2597468685,12684628125,62002335160,303332650190,
%U A128743 1485213237135,7277719953415,35687662907750,175120787451540
%N A128743 Number of UU's (i.e. doublerises) in all skew Dyck paths of semilength 
               n. A skew Dyck path is a path in the first quadrant which begins 
               at the origin, ends on the x-axis, consists of steps U=(1,1)(up), 
               D=(1,-1)(down) and L=(-1,-1) (left) so that up and left steps do 
               not overlap. The length of a path is defined to be the number of 
               its steps.
%C A128743 a(n)=Sum[k*A128718(n,k), k=0..n-1].
%D A128743 E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck paths (in preparation).
%F A128743 G.f.=[1-4z+z^2+(z-1)sqrt(1-6z+5z^2)]/[2z*sqrt(1-6z+5z^2)].
%e A128743 a(2)=2 because the paths of semilength 2 are UDUD, UUDD and UUDL, having 
               altogether 2 UU's.
%p A128743 G:=(1-4*z+z^2+(z-1)*sqrt(1-6*z+5*z^2))/2/z/sqrt(1-6*z+5*z^2): Gser:=series(G,
               z=0,30): seq(coeff(Gser,z,n),n=0..25);
%Y A128743 Cf. A128718.
%Y A128743 Sequence in context: A038144 A097977 A136780 this_sequence A097349 A109112 
               A163190
%Y A128743 Adjacent sequences: A128740 A128741 A128742 this_sequence A128744 A128745 
               A128746
%K A128743 nonn
%O A128743 0,3
%A A128743 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2007

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