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A165434
Number of tri-coverings of a set.
9
1, 1, 4, 39, 862, 35775, 2406208, 238773109, 32867762616, 6009498859909, 1412846181645855, 416415343791239162, 150747204270574506888, 65905473934553360340713, 34305461329980340135062217, 21003556204331356488142290707, 14967168378184553824642693791437
OFFSET
0,3
LINKS
E. A. Bender, Partitions of multisets, Discrete Mathematics 9 (1974) 301-312.
J. S. Devitt and D. M. Jackson, The enumeration of covers of a finite set, J. London Math. Soc.(2) 25 (1982), 1-6.
Doron Zeilberger, In How Many Ways Can You Reassemble Several Russian Dolls?, has links to more terms and related sequences
Doron Zeilberger, In How Many Ways Can You Reassemble Several Russian Dolls?, arXiv:0909.3453 [math.CO], 2009.
Doron Zeilberger, BABUSHKAS; Local copy
EXAMPLE
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}}.
MAPLE
Do SeqBrn(3, n); in the Maple package BABUSHKAS (see links) where n+1 is the number of desired terms.
CROSSREFS
Row 3 of A188392.
Cf. A000110 (unicoverings), A020554 (bicoverings).
Sequence in context: A299426 A188418 A136653 * A348118 A341473 A086217
KEYWORD
nonn
AUTHOR
Doron Zeilberger, Sep 18 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 28 2009
STATUS
approved