A060486 - OEIS

%I #14 Dec 17 2018 02:25:01

%S 1,0,0,5,205,11301,904580,101173251,15207243828,2975725761202,

%T 738628553556470,227636079973503479,85554823285296622543,

%U 38621481302086460057613,20669385794052533823555309,12966707189875262685801947906,9441485712482676603570079314728

%N 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.

%H Andrew Howroyd, <a href="/A060486/b060486.txt">Table of n, a(n) for n = 0..100</a>

%F E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..inf}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).

%e There are 1 4-block tricovering, 3 5-block tricoverings and 1 6-block tricovering of a 3-set (cf. A060487), so a(3)=5.

%Y Row 3 of A188445.

%Y Cf. A006095, A060483-A060485, (row sums of) A060487, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.

%K nonn

%O 0,4

%A _Vladeta Jovovic_, Mar 20 2001

%E Terms a(11) and beyond from _Andrew Howroyd_, Dec 15 2018