A211351 Refined triangle A091867: T(n,k) is the number of noncrossing partitions of an n-set that are of type k (k-th integer partition, defined by A194602).

1, 1, 1, 1, 3, 1, 1, 6, 4, 2, 1, 1, 10, 10, 10, 5, 5, 1, 1, 15, 20, 30, 15, 30, 6, 5, 6, 3, 1, 1, 21, 35, 70, 35, 105, 21, 35, 42, 21, 7, 21, 7, 7, 1, 1, 28, 56, 140, 70, 280, 56, 140, 168, 84, 28, 168, 56, 56, 8, 14, 28, 28, 8, 8, 4, 1

Offset

1,5

Comments

The rows are counted from 1, the columns from 0.

Row lengths: 1,2,3,5,7,11... (partition numbers A000041)

Row sums: 1,2,5,14,42,132... (Catalan numbers A000108)

Row maxima: 1,1,3,6,10,30,105,280,756,2520,6930,18480 (A130760)

Distinct entries per row: 1,1,2,4,3,7,7,11,12,18,18,30

Rightmost columns are those from Pascal's triangle A007318 without the second one (i.e. triangle A184049). The other columns - (always?) without a 1 at the top - are multiples of these columns from Pascal's triangle; so actually only the top elements of each column are needed to calculate the other entries; these top elements are in A211361.

Links

Tilman Piesk, Rows n=1..12 of triangle, flattened

Tilman Piesk, Partition related number triangles

Crossrefs

Cf. A091867, A000108, A130760, A184049, A211361.

Sequence in context: A305059 A355996 A128101 * A124802 A211350 A178867

Adjacent sequences: A211348 A211349 A211350 * A211352 A211353 A211354

Keyword

tabf,nonn

Author

Tilman Piesk, Apr 09 2012

Status

approved