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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..34.

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.

Cf. A002218, A030019, A048143, A134954, A275307, A293510, A317631, A317632, A317634, A317635, A317672, A317677.

Sequence in context: A088338 A020890 A343892 * A031453 A179203 A102017

Adjacent sequences:  A317668 A317669 A317670 * A317672 A317673 A317674

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Aug 03 2018

STATUS

approved

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Last modified June 20 08:57 EDT 2021. Contains 345162 sequences. (Running on oeis4.)