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

 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.

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