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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums give A000108.

LINKS

Alois P. Heinz, Rows n = 0..10, flattened

FindStat - Combinatorial Statistic Finder, The number of elements smaller than the given Dyck path in the Tamari Order.

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

Cf. A000108, A000260.

Sequence in context: A221857 A133607 A103631 * A192517 A309896 A083856

Adjacent sequences:  A263188 A263189 A263190 * A263192 A263193 A263194

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

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)