login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060090 Number of ordered bicoverings of an unlabeled n-set. 13
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

Andrew Howroyd, Table of n, a(n) for n = 0..200

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} 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 } )

PROG

(PARI) seq(n)={my(m=3*n\2, y='y + O('y^(n+1))); Vec(subst(Pol(serlaplace(exp(-x - x^2*y/(2*(1-y)) + O(x*x^m))*sum(k=0, m, 1/(1-y)^binomial(k, 2)*x^k/k!))), x, 1))} \\ Andrew Howroyd, Jan 30 2020

CROSSREFS

Row n=2 of A331571.

Row sums of A060092.

Cf. A060069, A060070, A060051, A060052, A060053, A002718, A059443.

Sequence in context: A199544 A302117 A006555 * A052842 A333957 A307418

Adjacent sequences:  A060087 A060088 A060089 * A060091 A060092 A060093

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Feb 25 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 28 03:43 EST 2021. Contains 340490 sequences. (Running on oeis4.)