A318398 Number of triples of set partitions of {1,2,...,n} whose meet is {{1},{2},...,{n}}.

1, 7, 103, 2707, 110857, 6517129, 521167549, 54510591469, 7235648605909, 1190181847444189, 237953165658759679, 56905537750421669449, 16059682765076576965879, 5287171379685771887014489, 2010360123437921314268936809, 875173620070717892287441139989

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

a(n) = Sum_{k = 0..n} s(n,k)*B(k)^3 where s = A048994 and B = A000110.

Example

The a(2) = 7 triples:
  {{1},{2}} {{1},{2}} {{1},{2}}
  {{1},{2}} {{1},{2}}  {{1,2}}
  {{1},{2}}  {{1,2}}  {{1},{2}}
  {{1},{2}}  {{1,2}}   {{1,2}}
   {{1,2}}  {{1},{2}} {{1},{2}}
   {{1,2}}  {{1},{2}}  {{1,2}}
   {{1,2}}   {{1,2}}  {{1},{2}}

Mathematica

Table[Sum[StirlingS1[n, k]*BellB[k]^3, {k, 0, n}], {n, 10}]

Crossrefs

Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318391, A318393, A318399.

Sequence in context: A357347 A177752 A101746 * A318815 A195246 A280644

Adjacent sequences: A318395 A318396 A318397 * A318399 A318400 A318401

Keyword

nonn

Author

Gus Wiseman, Aug 25 2018

Status

approved