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%I #8 Aug 04 2018 06:41:29
%S 1,2,3,44,24,16,4983,940,300,125,7565342,154770,18000,4320,1296,
%T 2414249587694,318926314,3927105,363580,72030,16807,
%U 56130437054842366160898,135200580256336,10244647168,99187200,8028160,1376256,262144
%N Regular triangle where T(n,k) is the number of clutters (connected antichains) on n + 1 vertices with k maximal blobs (2-connected components).
%H Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.
%e Triangle begins:
%e 1
%e 2 3
%e 44 24 16
%e 4983 940 300 125
%e 7565342 154770 18000 4320 1296
%t blg={0,1,2,44,4983,7565342,2414249587694,56130437054842366160898} (* A275307 *);
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t 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}]
%Y Row sums are A048143. First column is A275307. Last column is A030019.
%Y Cf. A000272, A001187, A002218, A013922, A134954, A293510, A317631, A317632, A317634, A317635, A317671.
%K nonn,tabl
%O 1,2
%A _Gus Wiseman_, Aug 03 2018
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