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

1,8

Comments

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

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

Row sums: 1,2,3,6,10,28... (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.

Sequence in context: A008967 A345971 A211355 * A094189 A122771 A217710

Adjacent sequences: A211350 A211351 A211352 * A211354 A211355 A211356

Keyword

tabf,nonn

Author

Tilman Piesk, Apr 09 2012

Status

approved