

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
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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



