A317674 Regular triangle where T(n,k) is the number of antichains covering n vertices with k connected components.

1, 1, 1, 5, 3, 1, 84, 23, 6, 1, 6348, 470, 65, 10, 1, 7743728, 39598, 1575, 145, 15, 1, 2414572893530, 54354104, 144403, 4095, 280, 21, 1, 56130437190053299918162, 19316801997024, 218033088, 402073, 9100, 490, 28, 1

Offset

1,4

Links

Table of n, a(n) for n=1..36.

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Example

Triangle begins:
        1
        1       1
        5       3       1
       84      23       6       1
     6348     470      65      10       1
  7743728   39598    1575     145      15       1

Mathematica

blg={1, 1, 5, 84, 6348, 7743728, 2414572893530, 56130437190053299918162} (*A048143*);
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Sum[Product[blg[[Length[s]]], {s, spn}], {spn, Select[sps[Range[n]], Length[#]==k&]}], {n, Length[blg]}, {k, n}]

Crossrefs

First column is A048143. Row sums are A006126.

Cf. A000272, A001187, A013922, A030019, A134954, A143543, A275307, A293510.

Cf. A317634, A317635, A317671, A317672, A317677.

Sequence in context: A114344 A350191 A350041 * A201333 A382483 A391752

Adjacent sequences: A317671 A317672 A317673 * A317675 A317676 A317677

Keyword

nonn,tabl

Author

Gus Wiseman, Aug 03 2018

Status

approved