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A211351 Refined triangle A091867: T(n,k) is the number of noncrossing partitions of an n-set that are of type k (k-th integer partition, defined by A194602).

%I A211351 #10 Apr 18 2012 15:47:34
%S A211351 1,1,1,1,3,1,1,6,4,2,1,1,10,10,10,5,5,1,1,15,20,30,15,30,6,5,6,3,1,1,
%T A211351 21,35,70,35,105,21,35,42,21,7,21,7,7,1,1,28,56,140,70,280,56,140,168,
%U A211351 84,28,168,56,56,8,14,28,28,8,8,4,1
%N A211351 Refined triangle A091867: T(n,k) is the number of noncrossing partitions of an n-set that are of type k (k-th integer partition, defined by A194602).
%C A211351 The rows are counted from 1, the columns from 0.
%C A211351 Row lengths: 1,2,3,5,7,11... (partition numbers A000041)
%C A211351 Row sums: 1,2,5,14,42,132... (Catalan numbers A000108)
%C A211351 Row maxima: 1,1,3,6,10,30,105,280,756,2520,6930,18480 (A130760)
%C A211351 Distinct entries per row: 1,1,2,4,3,7,7,11,12,18,18,30
%C A211351 Rightmost columns are those from Pascal's triangle A007318 without the second one (i.e. triangle A184049). The other columns - (always?) without a 1 at the top - are multiples of these columns from Pascal's triangle; so actually only the top elements of each column are needed to calculate the other entries; these top elements are in A211361.
%H A211351 Tilman Piesk, <a href="/A211351/b211351.txt">Rows n=1..12 of triangle, flattened</a>
%H A211351 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Partition_related_number_triangles#all1">Partition related number triangles</a>
%Y A211351 Cf. A091867, A000108, A130760, A184049, A211361.
%K A211351 tabf,nonn
%O A211351 1,5
%A A211351 _Tilman Piesk_, Apr 09 2012