A211355 Refined triangle A211359: T(n,k) is the number of noncrossing partitions up to rotation and reflection of an n-set that are of type k (k-th integer partition, defined by A194602).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 3, 5, 3, 3, 1, 2, 1, 1, 1, 1, 3, 4, 8, 4, 9, 3, 4, 4, 2, 1, 3, 1, 1, 1, 1, 4, 5, 14, 8, 19, 5, 14, 13, 8, 4, 12, 4, 4, 1, 3, 4, 3, 1, 1, 1, 1, 1, 4, 7, 20, 10, 38, 10, 30, 32, 16, 7, 48

Offset

1,8

Comments

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

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

Row sums: 1,2,3,6,10,24... (A111275)

Row maxima: 1,1,1,2,2,5,9,19,48,132,330,781

Distinct entries per row: 1,1,1,2,2,4,6,9,15,21,28,43

Rightmost columns are those from the triangle A052307 without the second column.

Links

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

Tilman Piesk, Partition related number triangles

Crossrefs

Cf. A211359, A000041, A111275, A052307.

Sequence in context: A373269 A008967 A345971 * A211353 A094189 A122771

Adjacent sequences: A211352 A211353 A211354 * A211356 A211357 A211358

Keyword

tabf,nonn

Author

Tilman Piesk, Apr 09 2012

Status

approved