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 A024482 a(n) = (1/2)*(binomial(2n, n) - binomial(2n-2, n-1)). 5
 2, 7, 25, 91, 336, 1254, 4719, 17875, 68068, 260338, 999362, 3848222, 14858000, 57500460, 222981435, 866262915, 3370764540, 13135064250, 51250632510, 200205672810, 782920544640, 3064665881940, 12007086477750, 47081501377326 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Apparently the number of sawtooth patterns in all Dyck paths of semilength n, ([0,1],2,7,25,...). A sawtooth pattern is of the form (UD)^k, k >= 1. More generally, the number of sawtooth patterns of length > t in all Dyck paths with semilength (n+t), t >= 0. - David Scambler, Apr 23 2013 LINKS FORMULA a(n) = A051924(n)/2. - Zerinvary Lajos, Jan 16 2007 From R. J. Mathar, Nov 09 2018: (Start) n*a(n) + (-5*n+4)*a(n-1) + 2*(2*n-5)*a(n-2) = 0. n*(3*n-5)*a(n) - 2*(3*n-2)*(2*n-3)*a(n-1) = 0. (End) EXAMPLE The path udUududD has two sawtooth patterns, shown in lower case. MAPLE Z:=(1-z-sqrt(1-4*z))/sqrt(1-4*z)/2: Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=2..25); # Zerinvary Lajos, Jan 16 2007 MATHEMATICA Table[(Binomial[2n, n]-Binomial[2n-2, n-1])/2, {n, 2, 30}] (* Harvey P. Dale, Mar 04 2011 *) CROSSREFS Cf. A097613, A225015. Sequence in context: A018907 A052936 A108152 * A097613 A074605 A292613 Adjacent sequences:  A024479 A024480 A024481 * A024483 A024484 A024485 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)