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%I #8 Jan 30 2020 16:36:03
%S 0,0,60,375,1392,4020,9960,22200,45730,88543,163000,287650,489610,
%T 807625,1295944,2029165,3108220,4667690,6884660,9989345,14277740,
%U 20126570,28010840,38524310,52403246,70553825,94083600,124337460,162938550,211834647,273350520,350246835
%N Number of 5-block ordered tricoverings of an unlabeled n-set.
%C A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
%H Andrew Howroyd, <a href="/A060489/b060489.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = binomial(n+9, 9) - 15*binomial(n+3, 3) + 45*binomial(n+1, 1) - 40*binomial(n, 0) + 9*binomial(n-1, -1).
%F G.f.: y^3*(-225*y^3 + 60 - 225*y + 342*y^2 + 90*y^5 - 50*y^6 + 9*y^7)/(-1+y)^10.
%F E.g.f. for ordered k-block tricoverings of an unlabeled n-set is exp(-x+x^2/2+x^3/3*y/(1-y))*Sum_{k>=0} 1/(1-y)^binomial(k, 3)*exp(-x^2/2*1/(1-y)^n)*x^k/k!.
%Y Column k=5 of A060492.
%Y Cf. A060093, A060483, A060491.
%K nonn
%O 1,3
%A _Vladeta Jovovic_, Mar 20 2001
%E a(1)=a(2)=0 prepended and terms a(30) and beyond from _Andrew Howroyd_, Jan 30 2020
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