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A317671
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Regular triangle where T(n,k) is the number of labeled connected graphs on n + 1 vertices with k maximal blobs (2-connected components).
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3
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Triangle begins:
1
1 3
10 12 16
238 215 150 125
11368 7740 4140 2160 1296
1014888 509446 205065 84035 36015 16807
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A002218, A030019, A048143, A134954, A275307, A293510, A317631, A317632, A317634, A317635, A317672, A317677.
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KEYWORD
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AUTHOR
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STATUS
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approved
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