A165434 Number of tri-coverings of a set.

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

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) 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

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