|
%I #9 Aug 04 2018 06:41:19
%S 1,1,3,10,12,16,238,215,150,125,11368,7740,4140,2160,1296,1014888,
%T 509446,205065,84035,36015,16807,166537616,59409952,17393152,5393920,
%U 1863680,688128,262144,50680432112,12321597708,2516756508,563570217,148803480,45467730
%N Regular triangle where T(n,k) is the number of labeled connected graphs on n + 1 vertices with k maximal blobs (2-connected components).
%e Triangle begins:
%e 1
%e 1 3
%e 10 12 16
%e 238 215 150 125
%e 11368 7740 4140 2160 1296
%e 1014888 509446 205065 84035 36015 16807
%t blg={0,1,1,10,238,11368,1014888,166537616,50680432112,29107809374336} (*A013922*);
%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 A001187. First column is A013922. Last column is A000272.
%Y Cf. A002218, A030019, A048143, A134954, A275307, A293510, A317631, A317632, A317634, A317635, A317672, A317677.
%K nonn,tabl
%O 1,3
%A _Gus Wiseman_, Aug 03 2018
|
