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).

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

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: A343892 A358892 A358893 * A031453 A345961 A179203

Adjacent sequences: A317668 A317669 A317670 * A317672 A317673 A317674

Keyword

nonn,tabl

Author

Gus Wiseman, Aug 03 2018

Status

approved