

A165434


Number of tricoverings of a set.


7



1, 1, 4, 39, 862, 35775, 2406208, 238773109, 32867762616, 6009498859909, 1412846181645855, 416415343791239162, 150747204270574506888, 65905473934553360340713, 34305461329980340135062217, 21003556204331356488142290707, 14967168378184553824642693791437
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OFFSET

0,3


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..100
E. A. Bender, Partitions of multisets, Discrete Mathematics 9 (1974) 301312.
J. S. Devitt and D. M. Jackson, The enumeration of covers of a finite set, J. London Math. Soc.(2) 25 (1982), 16.
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


EXAMPLE

For n=2, a(2)=4, since if you have two sets of identical triples the Abrothers and the Bsisters, 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 * A086217 A203197 A094156
Adjacent sequences: A165431 A165432 A165433 * A165435 A165436 A165437


KEYWORD

nonn


AUTHOR

Doron Zeilberger, Sep 18 2009


EXTENSIONS

Edited by Charles R Greathouse IV, Oct 28 2009


STATUS

approved



