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

0,11

Links

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

Example

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)

Prog

(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

Crossrefs

Column k=0 is A303931.

Row sums are A111275.

Cf. A209612, A211357, A303875.

Sequence in context: A049986 A218797 A137289 * A211357 A238416 A370852

Adjacent sequences: A211356 A211357 A211358 * A211360 A211361 A211362

Keyword

nonn,tabl

Author

Tilman Piesk, Apr 12 2012

Status

approved