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%I #7 Apr 18 2012 15:49:38
%S 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,
%T 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,
%U 1,4,7,20,10,38,10,30,32,16,7,48
%N 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).
%C The rows are counted from 1, the columns from 0.
%C Row lengths: 1,2,3,5,7,11... (partition numbers A000041)
%C Row sums: 1,2,3,6,10,24... (A111275)
%C Row maxima: 1,1,1,2,2,5,9,19,48,132,330,781
%C Distinct entries per row: 1,1,1,2,2,4,6,9,15,21,28,43
%C Rightmost columns are those from the triangle A052307 without the second column.
%H Tilman Piesk, <a href="/A211355/b211355.txt">Rows n=1..12 of triangle, flattened</a>
%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Partition_related_number_triangles#rotref1">Partition related number triangles</a>
%Y Cf. A211359, A000041, A111275, A052307.
%K tabf,nonn
%O 1,8
%A _Tilman Piesk_, Apr 09 2012
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