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A060090 Number of ordered bicoverings of an unlabeled n-set. 15
1, 0, 3, 23, 290, 4298, 79143, 1702923, 42299820, 1188147639, 37276597020, 1291633545897, 48995506718702, 2019395409175529, 89864601931874318, 4294295828157319651, 219321170795303112118, 11922219151375200468886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

E.g.f. for ordered k-block bicoverings of an unlabeled n-set is exp(-x-x^2/2*y/(1-y))*Sum_{k=0..inf} 1/(1-y)^binomial(k, 2)*x^k/k!.

EXAMPLE

There are 23 ordered bicoverings of an unlabeled 3-set, 7 3-block bicoverings:

1 ( { 3 }, { 1, 2 }, { 1, 2, 3 } )

2 ( { 3 }, { 1, 2, 3 }, { 1, 2 } )

3 ( { 2, 3 }, { 1 }, { 1, 2, 3 } )

4 ( { 2, 3 }, { 1, 3 }, { 1, 2 } )

5 ( { 2, 3 }, { 1, 2, 3 }, { 1 } )

6 ( { 1, 2, 3 }, { 3 }, { 1, 2 } )

7 ( { 1, 2, 3 }, { 2, 3 }, { 1 } )

and 16 4-block bicoverings:

1 ( { 3 }, { 2 }, { 1 }, { 1, 2, 3 } )

2 ( { 3 }, { 2 }, { 1, 3 }, { 1, 2 } )

3 ( { 3 }, { 2 }, { 1, 2 }, { 1, 3 } )

4 ( { 3 }, { 2 }, { 1, 2, 3 }, { 1 } )

5 ( { 3 }, { 2, 3 }, { 1 }, { 1, 2 } )

6 ( { 3 }, { 2, 3 }, { 1, 2 }, { 1 } )

7 ( { 3 }, { 1, 2 }, { 2 }, { 1, 3 } )

8 ( { 3 }, { 1, 2 }, { 2, 3 }, { 1 } )

9 ( { 3 }, { 1, 2, 3 }, { 2 }, { 1 } )

10 ( { 2, 3 }, { 3 }, { 1 }, { 1, 2 } )

11 ( { 2, 3 }, { 3 }, { 1, 2 }, { 1 } )

12 ( { 2, 3 }, { 1 }, { 3 }, { 1, 2 } )

13 ( { 2, 3 }, { 1 }, { 1, 3 }, { 2 } )

14 ( { 2, 3 }, { 1, 3 }, { 2 }, { 1 } )

15 ( { 2, 3 }, { 1, 3 }, { 1 }, { 2 } )

16 ( { 1, 2, 3 }, { 3 }, { 2 }, { 1 } )

CROSSREFS

Cf. A060091-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.

Sequence in context: A199544 A302117 A006555 * A052842 A307418 A231788

Adjacent sequences:  A060087 A060088 A060089 * A060091 A060092 A060093

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Feb 25 2001

STATUS

approved

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)