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%I #10 Jan 17 2020 17:45:06
%S 1,7,103,2773,117697,7167619,590978941,63385879261,8584707943381,
%T 1434654097736101,290409845948305321,70125579500764771585,
%U 19940633217840575968969,6603748351832744611210549,2522614472277243822293033719,1102166886808604068546379343289
%N Number of triples of set partitions of {1,2,...,n} whose join is {{1,2,...,n}}.
%H Alois P. Heinz, <a href="/A318815/b318815.txt">Table of n, a(n) for n = 1..233</a>
%F Logarithmic transform of A000110(n)^3.
%F a(n) = Bell(n)^3 - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Bell(n-k)^3 * k * a(k). - _Ilya Gutkovskiy_, Jan 17 2020
%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 nn=10;Table[n!*SeriesCoefficient[Log[1+Sum[BellB[n]^3*x^n/n!,{n,nn}]],{x,0,n}],{n,nn}]
%Y Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318391, A318393, A318398, A318399.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 04 2018
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