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Number of 6-block ordered bicoverings of an unlabeled n-set.
3

%I #15 Jan 30 2020 14:24:31

%S 0,0,0,0,90,1716,11350,49860,173745,519345,1389078,3411060,7821950,

%T 16949910,35013240,69404416,132703770,245767890,442372300,776064960,

%U 1330117230,2231754820,3672227850,5934754020,9432962515,14763202395

%N Number of 6-block ordered bicoverings of an unlabeled n-set.

%H Harry J. Smith, <a href="/A060094/b060094.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = binomial(n+14, n) - 6*binomial(n+9, 9) - 15*binomial(n+6, 6) + 30*binomial(n+5, 5) + 60*binomial(n+3, 3) - 50*binomial(n+2, 2) - 180*binomial(n+1, 1) + 240*binomial(n, 0) - 80*binomial(n-1, -1).

%F G.f.: -y^4*(366*y - 16950*y^8 + 36420*y^7 - 54120*y^6 + 56290*y^5 - 40335*y^4 + 18840*y^3 - 4940*y^2 - 960*y^10 + 80*y^11 + 5220*y^9 + 90)/(-1 + y)^15.

%F E.g.f. for k-block ordered 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!.

%o (PARI) a(n) = if(n<1, 0, binomial(n + 14, n) - 6*binomial(n + 9, 9) - 15*binomial(n + 6, 6) + 30*binomial(n + 5, 5) + 60*binomial(n + 3, 3) - 50*binomial(n + 2, 2) - 180*binomial(n + 1, 1) + 240*binomial(n, 0) - 80*binomial(n - 1, -1)) \\ _Harry J. Smith_, Jul 01 2009

%Y Column k=6 of A060092.

%Y Cf. A059947, A060090, A060490.

%K nonn

%O 0,5

%A _Vladeta Jovovic_, Feb 26 2001