A318399 Number of triples of set partitions of {1,...,n} with meet {{1},...,{n}} and join {{1,...,n}}.

1, 6, 84, 2226, 93246, 5616492, 459173406, 48933260388, 6595445513412, 1098326915060730, 221772386369110242, 53460963703982862534, 15185890964240671486740, 5026315912246843181692776, 1919721040169845172603949966, 838872819016448052585038291124

Offset: 1

Author

Gus Wiseman, Aug 25 2018

Keywords

• nonn

Examples

			The a(2) = 6 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}}
		

Crossrefs

Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318390, A318391, A318392, A318393, A318398.

Programs

Mathematica

nn=20;
Table[n!*SeriesCoefficient[Log[1+Sum[x^k/k!*Sum[StirlingS1[k,i]*BellB[i]^3,{i,0,k}],{k,nn}]],{x,0,n}],{n,nn}]

Formula

Logarithmic transform of A318398.