|
%I #9 Jan 22 2023 20:45:12
%S 1,7,103,2707,110857,6517129,521167549,54510591469,7235648605909,
%T 1190181847444189,237953165658759679,56905537750421669449,
%U 16059682765076576965879,5287171379685771887014489,2010360123437921314268936809,875173620070717892287441139989
%N Number of triples of set partitions of {1,2,...,n} whose meet is {{1},{2},...,{n}}.
%F a(n) = Sum_{k = 0..n} s(n,k)*B(k)^3 where s = A048994 and B = A000110.
%e The a(2) = 7 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}}
%e {{1,2}} {{1,2}} {{1},{2}}
%t Table[Sum[StirlingS1[n,k]*BellB[k]^3,{k,0,n}],{n,10}]
%Y Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318391, A318393, A318399.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 25 2018
|
