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 A059530 Triangle T(n,k) of k-block T_0-tricoverings of an n-set. 2

%I

%S 0,0,0,0,1,3,1,0,0,0,0,1,39,89,43,3,0,0,0,0,0,252,2192,4090,2435,445,

%T 12,0,0,0,0,0,1260,37080,179890,289170,188540,50645,4710,70,0,0,0,0,0,

%U 5040,536760,6052730,20660055,29432319,19826737,6481160,964495,52430

%N Triangle T(n,k) of k-block T_0-tricoverings of an 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. 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 <a href="/A060070/a060070.pdf">T_0-tricoverings of a 4-set</a>

%F E.g.f. for k-block T_0-tricoverings of an n-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!.

%e [0, 0, 0, 0, 1, 3, 1], [0, 0, 0, 0, 1, 39, 89, 43, 3], [0, 0, 0, 0, 0, 252, 2192, 4090, 2435, 445, 12], [0, 0, 0, 0, 0, 1260, 37080, 179890, 289170, 188540, 50645, 4710, 70], ...; there are 5=1+3+1 T_0-tricoverings of a 3-set and 175=1+39+89+43+3 T_0-tricoverings of a 4-set, cf. A060070.

%Y Cf. (column sums) A060069, (row sums) A060070, A060051-A060053, A002718, A059443, A003462, A059945-059951.

%K nonn,tabf

%O 3,6

%A _Vladeta Jovovic_, Feb 22 2001

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Last modified March 20 19:57 EDT 2019. Contains 321349 sequences. (Running on oeis4.)