A303868 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation and reflection with k paths and isolated vertices allowed.

1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 7, 6, 2, 1, 6, 20, 23, 11, 3, 1, 10, 50, 80, 51, 17, 3, 1, 20, 136, 285, 252, 109, 26, 4, 1, 36, 346, 966, 1119, 652, 200, 36, 4, 1, 72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1, 136, 2264, 10133, 19116, 18489, 9949, 3120, 570, 65, 5, 1

Offset: 1

Author

Andrew Howroyd, May 01 2018

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   1,   1;
   1,   1,    1;
   2,   3,    2,    1;
   3,   7,    6,    2,    1;
   6,  20,   23,   11,    3,    1;
  10,  50,   80,   51,   17,    3,   1;
  20, 136,  285,  252,  109,   26,   4,  1;
  36, 346,  966, 1119,  652,  200,  36,  4, 1;
  72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Row sums are A303835.

Column 1 is A005418(n-2).

Cf. A302828, A303869.

Programs

PARI

\\ See A303731 for NCPathSetsModDihedral
{ my(rows=Vec(NCPathSetsModDihedral(vector(10, k, y))-1));
  for(n=1, #rows, for(k=1, n, print1(polcoeff(rows[n],k), ", ")); print;) }