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

Author

Gus Wiseman, Aug 03 2018

Keywords

• nonn
• tabl

Examples

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

Links

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

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.

Programs

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}]