A003466 Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover.

0, 3, 28, 210, 1506, 10871, 80592, 618939, 4942070, 41076508, 355372524, 3198027157, 29905143464, 290243182755, 2920041395248, 30414515081650, 327567816748638, 3643600859114439, 41809197852127240, 494367554679088923, 6017481714095327410

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Robert Israel, Table of n, a(n) for n = 2..510
• T. Hearne and C. G. Wagner, Minimal covers of finite sets, Discr. Math. 5 (1973), 247-251.

Crossrefs

Cf. A046165.

Column k=1 of A282575.

Programs

Maple

seq(n*add((2^k-k-1)*Stirling2(n-1,k),k=1..n-1), n = 2 .. 30); # Robert Israel, May 21 2015

Mathematica

nn = 20; Range[0, nn]! CoefficientList[Series[Sum[ (Exp[x] - 1)^n/n! (2^n - n - 1) x, {n, 0, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Feb 18 2017 *)
a[2]=0;a[3]=3;a[4]=28;a[n_]:=n*Sum[(2^k-k-1)* StirlingS2[n-1,k], {k,1,n-1}];Table[a[n],{n,2,22}] (* Indranil Ghosh, Feb 20 2017 *)

Formula

a(n) = n * Sum_{k=1..n-1} (2^k-k-1) * S2(n-1,k) where S2(n,k) are the Stirling numbers of the second kind. - Sean A. Irvine, May 20 2015

a(n) = n * (A001861(n-1) - A005493(n-2) - A000110(n-1)). - Robert Israel, May 21 2015

Extensions

More terms from Sean A. Irvine, May 20 2015

Title clarified by Geoffrey Critzer, Feb 18 2017