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A263191
Triangle read by rows: T(n>=0, 1<=k<=A000108(n)) is the number of Dyck paths of length 2n having k smaller elements in Tamari order.
2
1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 3, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 4, 3, 5, 4, 2, 4, 0, 5, 2, 0, 2, 0, 3, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 4, 9, 6, 7, 6, 3, 10, 6, 4, 4, 0, 9, 5, 2, 0, 4, 4, 4, 0, 0, 4, 3, 1, 0, 2, 4, 0, 4, 0, 0, 0, 3, 0, 0, 2
OFFSET
0,6
COMMENTS
Row sums give A000108.
LINKS
Wikipedia, Tamari lattice.
FORMULA
Sum_{k=1..A000108(n)} k * T(n,k) = A000260(n). - Alois P. Heinz, Nov 15 2015
EXAMPLE
Triangle begins:
1;
1;
1,1;
1,2,1,0,1;
1,3,2,2,2,0,2,0,1,0,0,0,0,1;
1,4,3,5,4,2,4,0,5,2,0,2,0,3,0,1,0,0,2,0,0,0,2,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,1;
...
CROSSREFS
Sequence in context: A133607 A103631 A374176 * A192517 A309896 A083856
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Oct 19 2015
EXTENSIONS
Two terms (for rows 0 and 1) prepended by Alois P. Heinz, Nov 15 2015
STATUS
approved