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A322441 Number of pairs of set partitions of {1,...,n} where no block of one is a subset or equal to any block of the other. 7
1, 0, 0, 0, 6, 60, 630, 9660, 192906 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

The a(4) = 6 pairs of set partitions:

  {{1,2},{3,4}}|{{1,3},{2,4}}

  {{1,2},{3,4}}|{{1,4},{2,3}}

  {{1,3},{2,4}}|{{1,2},{3,4}}

  {{1,3},{2,4}}|{{1,4},{2,3}}

  {{1,4},{2,3}}|{{1,2},{3,4}}

  {{1,4},{2,3}}|{{1,3},{2,4}}

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

stabQ[u_]:=stabQ[u, SubsetQ]; stabQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

Table[Length[Select[Tuples[sps[Range[n]], 2], And[UnsameQ@@Join@@#, stabQ[Join@@#]]&]], {n, 6}]

CROSSREFS

Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A321760 (unlabeled version), A322435, A322442.

Sequence in context: A136893 A090019 A186676 * A186674 A186672 A295503

Adjacent sequences:  A322438 A322439 A322440 * A322442 A322443 A322444

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 4 14:29 EDT 2020. Contains 335448 sequences. (Running on oeis4.)