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A060483
Number of 5-block tricoverings of an n-set.
6
3, 57, 717, 7845, 81333, 825237, 8300757, 83202645, 832809813, 8331237717, 83324947797, 833299785045, 8333199127893, 83332796486997, 833331185898837, 8333324743497045, 83333298973791573, 833333195894773077, 8333332783578305877, 83333331134311650645
OFFSET
3,1
COMMENTS
A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
FORMULA
a(n) = (1/5!)*(10^n - 15*4^n + 45*2^n - 40).
Generally, 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).
G.f.: 3*x^3*(2*x+1) / ((x-1)*(2*x-1)*(4*x-1)*(10*x-1)). - Colin Barker, Jan 11 2013
PROG
(PARI) Vec(3*(1+2*x)/(x-1)/(2*x-1)/(4*x-1)/(10*x-1)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2013
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Mar 20 2001
EXTENSIONS
More terms from Colin Barker, Jan 11 2013
STATUS
approved