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%I #9 Jan 31 2020 14:34:57
%S 1,0,0,0,2,82194,9185157387760082,
%T 5573096894405951375691132323893805593,
%U 47933892393105239218152796441416602126447041437452022947424986090407628
%N Number of n-block T_0-tricoverings.
%C A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering; A covering of a set is a T_0-covering if for every two distinct elements of the set there exists a block of the covering containing one but not the other element.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
%H Andrew Howroyd, <a href="/A060069/b060069.txt">Table of n, a(n) for n = 0..15</a>
%F E.g.f. for n-block T_0-tricoverings of a k-set is exp(-x+1/2*x^2+1/3*x^3*y)*Sum_{i=0..inf} (1+y)^binomial(i, 3)*exp(-1/2*x^2*(1+y)^i)*x^i/i!.
%Y Column sums of A059530.
%Y Cf. A060051, A060053, A060070, A060486.
%K nonn
%O 0,5
%A _Vladeta Jovovic_, Feb 19 2001
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