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%I #32 Mar 28 2021 23:56:14
%S 1,1,4,39,862,35775,2406208,238773109,32867762616,6009498859909,
%T 1412846181645855,416415343791239162,150747204270574506888,
%U 65905473934553360340713,34305461329980340135062217,21003556204331356488142290707,14967168378184553824642693791437
%N Number of tri-coverings of a set.
%H Andrew Howroyd, <a href="/A165434/b165434.txt">Table of n, a(n) for n = 0..100</a>
%H E. A. Bender, <a href="http://dx.doi.org/10.1016/0012-365X(74)90076-4">Partitions of multisets</a>, Discrete Mathematics 9 (1974) 301-312.
%H J. S. Devitt and D. M. Jackson, <a href="http://dx.doi.org/10.1112/jlms/s2-25.1.1">The enumeration of covers of a finite set</a>, J. London Math. Soc.(2) 25 (1982), 1-6.
%H Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/babushkas.html">In How Many Ways Can You Reassemble Several Russian Dolls?</a>, has links to more terms and related sequences
%H Doron Zeilberger, <a href="http://arxiv.org/abs/0909.3453">In How Many Ways Can You Reassemble Several Russian Dolls?</a>, arXiv:0909.3453 [math.CO], 2009.
%H Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/tokhniot/BABUSHKAS">BABUSHKAS</a>; <a href="/A165434/a165434.txt">Local copy</a>
%e For n=2, a(2)=4, since if you have two sets of identical triples the A-brothers and the B-sisters, and you want to arrange them into a multiset of nonempty sets, where no one is allowed to cohabitate with his or her sibling, the following are possible 1.{{AB},{AB},{AB}} 2.{{AB},{AB},{A},{B}} 3.{{AB},{A},{A},{B},{B}} 4.{{A},{A},{A},{B},{B},{B}}.
%p Do SeqBrn(3,n); in the Maple package BABUSHKAS (see links) where n+1 is the number of desired terms.
%Y Row 3 of A188392.
%Y Cf. A000110 (unicoverings), A020554 (bicoverings).
%K nonn
%O 0,3
%A _Doron Zeilberger_, Sep 18 2009
%E Edited by _Charles R Greathouse IV_, Oct 28 2009
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