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

Author

Tilman Piesk, Apr 09 2012

Keywords

• tabf
• nonn

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.