A211353 Refined triangle A211357: T(n,k) is the number of noncrossing partitions up to rotation 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, 4, 6, 3, 5, 1, 2, 1, 1, 1, 1, 3, 5, 10, 5, 15, 3, 5, 6, 3, 1, 3, 1, 1, 1, 1, 4, 7, 19, 10, 35, 7, 19, 21, 12, 4, 21, 7, 7, 1, 3, 4, 4, 1, 1, 1, 1, 1, 4, 10, 28, 14, 70, 14, 48, 56, 28, 10

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: 1,2,3,6,10,28... (A054357)

Row maxima: 1,1,1,2,2,6,15,35,84,252,630,1542...

Distinct entries per row: 1,1,1,2,2,6,6,9,11,17,17,30...

Rightmost columns are those from the triangle of circular binomial coefficients A047996 without the second column (i.e.triangle A037306).

Links

• Tilman Piesk, Rows n=1..12 of triangle, flattened
• Tilman Piesk, Partition related number triangles

Crossrefs

Cf. A211357, A000041, A054357, A047996, A037306.