OFFSET
2,2
COMMENTS
Row sums give A000392.
LINKS
Robert Israel, Table of n, a(n) for n = 2..10012 (rows 2 to 142, flattened)
Octavio A. Agustín-Aquino, Archimedes' quadrature of the parabola and minimal covers, arXiv:1602.05279 [math.CO], 2016.
Eric Weisstein's World of Mathematics, Minimal cover
FORMULA
Number of minimal m-covers of a labeled n-set that cover k points of that set uniquely is C(n, k)*S(k, m)*(2^m-m-1)^(n-k), where S(k, m) are Stirling numbers of the second kind. Here m=2.
From Robert Israel, Feb 18 2016: (Start)
T(n,k) = C(n,k) * (2^(k-1)-1).
G.f. of triangle: x^2*y^2/((1-x)*(1-x-x*y)*(1-x-2*x*y)). (End)
EXAMPLE
There are 90=10+30+35+15 minimal 2-covers of a labeled 5-set.
Triangle starts:
1;
3, 3;
6, 12, 7;
10, 30, 35, 15;
15, 60, 105, 90, 31;
...
MAPLE
seq(seq(binomial(n, k)*(2^(k-1)-1), k=2..n), n=2..13); # Robert Israel, Feb 18 2016
MATHEMATICA
Table[ Binomial[n, k] (2^(k-1)-1), {n, 2, 13}, {k, 2, n}] // Flatten (* Jean-François Alcover, Sep 18 2018, from Maple *)
PROG
(PARI) T(n, k) = m=2; binomial(n, k)*stirling(k, m, 2)*(2^m-m-1)^(n-k); \\ Michel Marcus, Feb 18 2016
(Magma) /* As triangle: */ [[Binomial(n, k)*(2^(k-1)-1): k in [2..n]]: n in [1.. 15]]; // Vincenzo Librandi, Feb 19 2016
CROSSREFS
KEYWORD
AUTHOR
Vladeta Jovovic, Oct 17 2000
STATUS
approved