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A024482 a(n) = (1/2)*(C(2n,n) - C(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

Table of n, a(n) for n=2..25.

FORMULA

a(n) = A051924/2. - Zerinvary Lajos, Jan 16 2007

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. A225015.

Sequence in context: A018907 A052936 A108152 * A097613 A074605 A292613

Adjacent sequences:  A024479 A024480 A024481 * A024483 A024484 A024485

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 19 06:43 EDT 2018. Contains 315172 sequences. (Running on oeis4.)