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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
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
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.
Sequence in context: A123111 A346541 A303154 * A300590 A027873 A203529
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 21 2001
EXTENSIONS
Terms a(15) and beyond from Andrew Howroyd, Jan 08 2020
STATUS
approved