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%I #8 Apr 18 2012 15:48:40
%S 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,
%T 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,
%U 1,1,1,4,10,28,14,70,14,48,56,28,10
%N 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).
%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: 1,2,3,6,10,28... (A054357)
%C Row maxima: 1,1,1,2,2,6,15,35,84,252,630,1542...
%C Distinct entries per row: 1,1,1,2,2,6,6,9,11,17,17,30...
%C Rightmost columns are those from the triangle of circular binomial coefficients A047996 without the second column (i.e.triangle A037306).
%H Tilman Piesk, <a href="/A211353/b211353.txt">Rows n=1..12 of triangle, flattened</a>
%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Partition_related_number_triangles#rot1">Partition related number triangles</a>
%Y Cf. A211357, A000041, A054357, A047996, A037306.
%K tabf,nonn
%O 1,8
%A _Tilman Piesk_, Apr 09 2012
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