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 A060070 Number of T_0-tricoverings of an n-set. 14
 1, 0, 0, 5, 175, 9426, 751365, 84012191, 12644839585, 2479642897109, 617049443550205, 190678639438170502, 71860665148118443795, 32527628234581386962713, 17454341903042193018433239, 10978059489008346809004564072, 8013452442154510131205645967978 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 Vladeta Jovovic, T_0-tricoverings of a 4-set FORMULA 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!. a(n) = Sum_{k=0..n} Stirling1(n, k)*A060486(k). - Andrew Howroyd, Jan 08 2020 PROG (PARI) seq(n)={my(m=2*n, y='y + O('y^(n+1))); Vec(serlaplace(subst(Pol(exp(-x + x^2/2 + x^3*y/3 + O(x*x^m))*sum(k=0, m, (1+y)^binomial(k, 3)*exp(-x^2*(1+y)^k/2 + O(x*x^m))*x^k/k!)), x, 1)))} \\ Andrew Howroyd, Jan 30 2020 CROSSREFS Row n=3 of A331039. Row sums of A059530. Cf. A060051, A060053, A060069, A060486. Sequence in context: A139986 A123111 A303154 * A300590 A027873 A203529 Adjacent sequences:  A060067 A060068 A060069 * A060071 A060072 A060073 KEYWORD nonn AUTHOR Vladeta Jovovic, Feb 21 2001 EXTENSIONS Terms a(15) and beyond from Andrew Howroyd, Jan 08 2020 STATUS approved

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Last modified July 11 04:33 EDT 2020. Contains 335609 sequences. (Running on oeis4.)