A303869 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation with k paths and isolated vertices allowed.

1, 1, 1, 1, 1, 1, 3, 4, 2, 1, 4, 11, 8, 2, 1, 10, 34, 39, 16, 3, 1, 16, 92, 144, 90, 25, 3, 1, 36, 256, 545, 473, 197, 40, 4, 1, 64, 672, 1878, 2184, 1246, 370, 56, 4, 1, 136, 1762, 6296, 9436, 7130, 2910, 658, 80, 5, 1, 256, 4480, 20100, 38025, 36690, 19698, 6090, 1080, 105, 5, 1

Offset: 1

Author

Andrew Howroyd, May 01 2018

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    1,    1;
    1,    1,    1;
    3,    4,    2,    1;
    4,   11,    8,    2,    1;
   10,   34,   39,   16,    3,    1;
   16,   92,  144,   90,   25,    3,   1;
   36,  256,  545,  473,  197,   40,   4,  1;
   64,  672, 1878, 2184, 1246,  370,  56,  4, 1;
  136, 1762, 6296, 9436, 7130, 2910, 658, 80, 5, 1;
  ...
		

Links

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

Crossrefs

Row sums are A303836.

Column 1 is A051437(n-3).

Cf. A303844, A303732, A303864, A303868.

Programs

PARI

\\ See A303732 for NCPathSetsModCyclic
{ my(rows=Vec(NCPathSetsModCyclic(vector(10, k, y))-1));
for(n=1, #rows, for(k=1,n,print1(polcoeff(rows[n],k), ", ")); print;)}