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

Author

Gus Wiseman, Aug 25 2018

Keywords

• nonn

Examples

			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}}
		

Crossrefs

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

Programs

Mathematica

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

Formula

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