A060090 - OEIS

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A060090

Number of ordered bicoverings of an unlabeled n-set.

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^2/2y/(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=3n\2, y='y + O('y^(n+1))); Vec(subst(Pol(serlaplace(exp(-x - x^2y/(2(1-y)) + O(xx^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`

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