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Triangle read by rows: T(n,k) is the number of noncrossing partitions up to rotation and reflection of an n-set that contain k singleton blocks.
5

%I #11 May 03 2018 17:02:52

%S 1,0,1,1,0,1,1,1,0,1,2,1,2,0,1,2,3,2,2,0,1,5,4,8,3,3,0,1,6,11,12,12,4,

%T 3,0,1,14,21,39,24,22,5,4,0,1,22,55,84,85,48,30,7,4,0,1,51,124,245,

%U 228,190,82,46,8,5,0,1,95,327,620,730,570,350,136,60

%N Triangle read by rows: T(n,k) is the number of noncrossing partitions up to rotation and reflection of an n-set that contain k singleton blocks.

%H Andrew Howroyd, <a href="/A211359/b211359.txt">Table of n, a(n) for n = 0..1274</a> (terms 0..90 from Tilman Piesk)

%e From _Andrew Howroyd_, May 02 2018: (Start)

%e Triangle begins:

%e 1;

%e 0, 1;

%e 1, 0, 1;

%e 1, 1, 0, 1;

%e 2, 1, 2, 0, 1;

%e 2, 3, 2, 2, 0, 1;

%e 5, 4, 8, 3, 3, 0, 1;

%e 6, 11, 12, 12, 4, 3, 0, 1;

%e 14, 21, 39, 24, 22, 5, 4, 0, 1;

%e 22, 55, 84, 85, 48, 30, 7, 4, 0, 1;

%e 51, 124, 245, 228, 190, 82, 46, 8, 5, 0, 1;

%e ...

%e (End)

%o (PARI) \\ See A303875 for NCPartitionsModDihedral

%o { my(rows=Vec(NCPartitionsModDihedral(vector(10, k, if(k==1,y,1)))));

%o for(n=1, #rows, for(k=0, n-1, print1(polcoeff(rows[n], k), ", ")); print; ) } \\ _Andrew Howroyd_, May 02 2018

%Y Column k=0 is A303931.

%Y Row sums are A111275.

%Y Cf. A209612, A211357, A303875.

%K nonn,tabl

%O 0,11

%A _Tilman Piesk_, Apr 12 2012