Search: id:A035929
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%I A035929
%S A035929 0,1,1,1,2,6,19,61,200,670,2286,7918,27770,98424,351983,
%T A035929 1268541,4602752,16799894,61642078,227239086,841230292,
%U A035929 3126039364,11656497518,43601626146,163561902392,615183356156
%N A035929 Number of Dyck paths starting U^mD^m (an m-pyramid), followed by a pyramid-free 
               Dyck path.
%C A035929 Hankel transform is -A128834. [From Paul Barry (pbarry(AT)wit.ie), Jul 
               04 2009]
%F A035929 G.f.: (2x)/(1+x + sqrt(1-4x)).
%F A035929 G.f. satisfies A^2*(x^2-2*x+2)-A*(x+1)+x = 0.
%F A035929 The generating function can be written as x/(1-x) times that of A082989.
%F A035929 G.f.: (2x)/(1+x+(1-x)*sqrt(1-4x)); 1/(1-x(1-x)/(1-x/(1-x/(1-x/(1-x/(1-x/
               (1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), 
               Jul 04 2009]
%e A035929 The a(5)=6 cases are UUUUUDDDDD, UDUUUDUDDD, UDUUUDDUDD, UDUUDUUDDDD, 
               UDUUDUDUDUDD and UUDDUUDUDD
%p A035929 A:= proc(n) option remember; if n=0 then 0 else convert (series ((A(n-1)^2 
               *(x^2-2*x+2) +x)/ (x+1), x,n+1), polynom) fi end: a:= n-> coeff (A(n), 
               x,n): seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 23 2008]
%Y A035929 Cf. A082989.
%Y A035929 Sequence in context: A022015 A138747 A052975 this_sequence A071646 A114627 
               A148464
%Y A035929 Adjacent sequences: A035926 A035927 A035928 this_sequence A035930 A035931 
               A035932
%K A035929 nonn
%O A035929 0,5
%A A035929 N. J. A. Sloane (njas(AT)research.att.com).
%E A035929 Edited by Lou Shapiro (lshapiro(AT)howard.edu), Feb 16 2005

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