login
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
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.
Sequence in context: A077520 A230061 A100015 * A352003 A356047 A042819
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 03 2018
STATUS
approved