A060070 Number of T_0-tricoverings of an n-set.

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

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: A123111 A346541 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