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A172101 Triangle, read by rows, given by [0,1,0,-1,0,1,0,-1,0,1,0,-1,0,...] DELTA [1,0,-1,0,1,0,-1,0,1,0,-1,0,1,...] where DELTA is the operator defined in A084938. 0
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 4, 2, 1, 0, 1, 3, 6, 6, 3, 1, 0, 1, 3, 9, 9, 9, 3, 1, 0, 1, 4, 12, 18, 18, 12, 4, 1, 0, 1, 4, 16, 24, 36, 24, 16, 4, 1, 0, 1, 5, 20, 40, 60, 60, 40, 20, 5, 1, 0, 1, 5, 25, 50, 100, 100, 100, 50, 25, 5, 1, 0, 1, 6, 30, 75, 150, 200, 200, 150 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Number of symmetric Dyck paths of semilength n with k peaks. Diagonal sums : A088518, row sums : A001405.

LINKS

Table of n, a(n) for n=0..86.

FORMULA

Sum_{k, 0<=k<=n} T(n,k) = A001405(n).

EXAMPLE

Triangle begins :

1 ;

0,1 ;

0,1,1 ;

0,1,1,1 ;

0,1,2,2,1 ;

0,1,2,4,2,1 ;

0,1,3,6,6,3,1 ; ...

CROSSREFS

Cf. A088855

Sequence in context: A098884 A039800 A251418 * A109246 A037890 A037898

Adjacent sequences:  A172098 A172099 A172100 * A172102 A172103 A172104

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jan 25 2010

STATUS

approved

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Last modified December 10 21:23 EST 2016. Contains 279011 sequences.