cp's OEIS Frontend

A317671 Regular triangle where T(n,k) is the number of labeled connected graphs on n + 1 vertices with k maximal blobs (2-connected components).

%I A317671 #9 Aug 04 2018 06:41:19
%S A317671 1,1,3,10,12,16,238,215,150,125,11368,7740,4140,2160,1296,1014888,
%T A317671 509446,205065,84035,36015,16807,166537616,59409952,17393152,5393920,
%U A317671 1863680,688128,262144,50680432112,12321597708,2516756508,563570217,148803480,45467730
%N A317671 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 A317671 Triangle begins:
%e A317671         1
%e A317671         1       3
%e A317671        10      12      16
%e A317671       238     215     150     125
%e A317671     11368    7740    4140    2160    1296
%e A317671   1014888  509446  205065   84035   36015   16807
%t A317671 blg={0,1,1,10,238,11368,1014888,166537616,50680432112,29107809374336} (*A013922*);
%t A317671 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A317671 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 A317671 Row sums are A001187. First column is A013922. Last column is A000272.
%Y A317671 Cf. A002218, A030019, A048143, A134954, A275307, A293510, A317631, A317632, A317634, A317635, A317672, A317677.
%K A317671 nonn,tabl
%O A317671 1,3
%A A317671 _Gus Wiseman_, Aug 03 2018