A003466 Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover. (Formerly M3117)

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

Offset

2,2

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.

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

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 *)

Crossrefs

Cf. A046165.

Column k=1 of A282575.

Sequence in context: A278183 A091120 A045737 * A337590 A092637 A338689

Adjacent sequences: A003463 A003464 A003465 * A003467 A003468 A003469

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, May 20 2015

Title clarified by Geoffrey Critzer, Feb 18 2017

Status

approved