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A317674 Regular triangle where T(n,k) is the number of antichains covering n vertices with k connected components. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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: A115991 A143410 A114344 * A201333 A088324 A052038

Adjacent sequences:  A317671 A317672 A317673 * A317675 A317676 A317677

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Aug 03 2018

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)