A263864 Triangle read by rows: T(n,k) (n>=1, k>=1) is the number of posets with n elements whose Hasse diagram has k connected components.

1, 1, 1, 3, 1, 1, 10, 4, 1, 1, 44, 13, 4, 1, 1, 238, 60, 14, 4, 1, 1, 1650, 312, 63, 14, 4, 1, 1, 14512, 2075, 328, 64, 14, 4, 1, 1, 163341, 17316, 2159, 331, 64, 14, 4, 1, 1, 2360719, 186173, 17801, 2175, 332, 64, 14, 4, 1, 1, 43944974, 2594568, 189406, 17885, 2178, 332, 64, 14, 4, 1, 1, 1055019099, 47041877

Offset

1,4

Comments

Multiset transformation of A000608.

Links

Alois P. Heinz, Rows n = 1..16, flattened

FindStat - Combinatorial Statistic Finder, The number of connected components of the Hasse diagram for the poset.

Salah Uddin Mohammad, Md. Shah Noor, and Md. Rashed Talukder, An Exact Enumeration of the Unlabeled Disconnected Posets, J. Int. Seq., Vol. 25 (2022), Article 22.5.4.

Wikipedia, Hasse diagram

Index entries for sequences related to posets

Example

Triangle begins:
   1;
   1,  1;
   3,  1,  1;
  10,  4,  1,  1;
  44, 13,  4,  1,  1;
  ...

Crossrefs

Cf. A000112 (row sums), A000608 (k=1).

Sequence in context: A268115 A106268 A267655 * A060543 A267751 A185996

Adjacent sequences: A263861 A263862 A263863 * A263865 A263866 A263867

Keyword

nonn,tabl

Author

Christian Stump, Oct 28 2015

Extensions

More terms from R. J. Mathar, Jul 12 2020

Status

approved