%I #11 Jan 30 2020 14:23:45

%S 1,0,3,23,290,4298,79143,1702923,42299820,1188147639,37276597020,

%T 1291633545897,48995506718702,2019395409175529,89864601931874318,

%U 4294295828157319651,219321170795303112118,11922219151375200468886

%N Number of ordered bicoverings of an unlabeled n-set.

%H Andrew Howroyd, <a href="/A060090/b060090.txt">Table of n, a(n) for n = 0..200</a>

%F 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!.

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

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

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

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

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

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

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

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

%e and 16 4-block bicoverings:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%o (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

%Y Row n=2 of A331571.

%Y Row sums of A060092.

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

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Feb 25 2001