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%I #5 Aug 27 2018 22:34:19
%S 1,6,84,2226,93246,5616492,459173406,48933260388,6595445513412,
%T 1098326915060730,221772386369110242,53460963703982862534,
%U 15185890964240671486740,5026315912246843181692776,1919721040169845172603949966,838872819016448052585038291124
%N Number of triples of set partitions of {1,...,n} with meet {{1},...,{n}} and join {{1,...,n}}.
%F Logarithmic transform of A318398.
%e The a(2) = 6 triples:
%e {{1},{2}} {{1},{2}} {{1,2}}
%e {{1},{2}} {{1,2}} {{1},{2}}
%e {{1},{2}} {{1,2}} {{1,2}}
%e {{1,2}} {{1},{2}} {{1},{2}}
%e {{1,2}} {{1},{2}} {{1,2}}
%e {{1,2}} {{1,2}} {{1},{2}}
%t nn=20;
%t 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}]
%Y Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318390, A318391, A318392, A318393, A318398.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 25 2018