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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).
3
1, 1, 3, 10, 12, 16, 238, 215, 150, 125, 11368, 7740, 4140, 2160, 1296, 1014888, 509446, 205065, 84035, 36015, 16807, 166537616, 59409952, 17393152, 5393920, 1863680, 688128, 262144, 50680432112, 12321597708, 2516756508, 563570217, 148803480, 45467730
OFFSET
1,3
EXAMPLE
Triangle begins:
1
1 3
10 12 16
238 215 150 125
11368 7740 4140 2160 1296
1014888 509446 205065 84035 36015 16807
MATHEMATICA
blg={0, 1, 1, 10, 238, 11368, 1014888, 166537616, 50680432112, 29107809374336} (*A013922*);
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 A001187. First column is A013922. Last column is A000272.
Sequence in context: A343892 A358892 A358893 * A031453 A345961 A179203
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 03 2018
STATUS
approved