A317672 Regular triangle where T(n,k) is the number of clutters (connected antichains) on n + 1 vertices with k maximal blobs (2-connected components).

1, 2, 3, 44, 24, 16, 4983, 940, 300, 125, 7565342, 154770, 18000, 4320, 1296, 2414249587694, 318926314, 3927105, 363580, 72030, 16807, 56130437054842366160898, 135200580256336, 10244647168, 99187200, 8028160, 1376256, 262144

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Example

Triangle begins:
        1
        2       3
       44      24      16
     4983     940     300     125
  7565342  154770   18000    4320    1296

Mathematica

blg={0, 1, 2, 44, 4983, 7565342, 2414249587694, 56130437054842366160898} (* A275307 *);
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Sum[n^(k-1)*Product[blg[[Length[s]+1]], {s, spn}], {spn, Select[sps[Range[n-1]], Length[#]==k&]}], {n, Length[blg]}, {k, n-1}]

Crossrefs

Row sums are A048143. First column is A275307. Last column is A030019.

Cf. A000272, A001187, A002218, A013922, A134954, A293510, A317631, A317632, A317634, A317635, A317671.

Sequence in context: A077520 A230061 A100015 * A352003 A356047 A042819

Adjacent sequences: A317669 A317670 A317671 * A317673 A317674 A317675

Keyword

nonn,tabl

Author

Gus Wiseman, Aug 03 2018

Status

approved