A211359 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.

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

Offset: 0

Author

Tilman Piesk, Apr 12 2012

Keywords

• nonn
• tabl

Examples

			From _Andrew Howroyd_, May 02 2018: (Start)
Triangle begins:
   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,  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, 228, 190, 82, 46, 8, 5, 0, 1;
  ...
(End)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1274 (terms 0..90 from Tilman Piesk)

Crossrefs

Column k=0 is A303931.

Row sums are A111275.

Cf. A209612, A211357, A303875.

Programs

PARI

\\ See A303875 for NCPartitionsModDihedral
{ my(rows=Vec(NCPartitionsModDihedral(vector(10, k, if(k==1,y,1)))));
for(n=1, #rows, for(k=0, n-1, print1(polcoeff(rows[n], k), ", ")); print; ) } \\ Andrew Howroyd, May 02 2018