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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 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: A039800 A309416 A251418 * A301365 A109246 A037890 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 September 24 07:49 EDT 2021. Contains 347623 sequences. (Running on oeis4.)