login
Refined triangle A211356: T(n,k) is the number of partitions up to rotation of an n-set that are of type k (k-th integer partition, defined by A194602).
1

%I #8 Apr 18 2012 15:48:09

%S 1,1,1,1,1,1,1,2,1,2,1,1,2,2,3,1,2,1,1,3,4,9,3,10,1,5,3,3,1,1,3,5,15,

%T 5,30,3,15,15,10,1,15,3,5,1,1,4,7,29,10,70,7,56,54,37,4,105,21,35,1,

%U 18,29,37,4,7,7,1

%N Refined triangle A211356: T(n,k) is the number of 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: 1,2,3,7,12,43... (A084423)

%C Row maxima: 1,1,1,2,3,10,30,105,420,1268,6300...

%C Distinct entries per row: 1,1,1,2,3,6,6,13,17,25,25...

%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="/A211352/b211352.txt">Rows n=1..11 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. A211356, A000041, A084423, A047996, A037306.

%K tabf,nonn

%O 1,8

%A _Tilman Piesk_, Apr 09 2012