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 A317672 Regular triangle where T(n,k) is the number of clutters (connected antichains) on n + 1 vertices with k maximal blobs (2-connected components). 15
 1, 2, 3, 44, 24, 16, 4983, 940, 300, 125, 7565342, 154770, 18000, 4320, 1296, 2414249587694, 318926314, 3927105, 363580, 72030, 16807, 56130437054842366160898, 135200580256336, 10244647168, 99187200, 8028160, 1376256, 262144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017. EXAMPLE Triangle begins:         1         2       3        44      24      16      4983     940     300     125   7565342  154770   18000    4320    1296 MATHEMATICA blg={0, 1, 2, 44, 4983, 7565342, 2414249587694, 56130437054842366160898} (* A275307 *); 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 A048143. First column is A275307. Last column is A030019. Cf. A000272, A001187, A002218, A013922, A134954, A293510, A317631, A317632, A317634, A317635, A317671. Sequence in context: A077520 A230061 A100015 * A042819 A218002 A255969 Adjacent sequences:  A317669 A317670 A317671 * A317673 A317674 A317675 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Aug 03 2018 STATUS approved

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Last modified September 15 16:44 EDT 2019. Contains 327078 sequences. (Running on oeis4.)