

A003466


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


2



0, 3, 28, 210, 1506, 10871, 80592, 618939, 4942070, 41076508, 355372524, 3198027157, 29905143464, 290243182755, 2920041395248, 30414515081650, 327567816748638, 3643600859114439, 41809197852127240, 494367554679088923, 6017481714095327410
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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), 247251.


FORMULA

a(n) = n * sum((2^kk1) * S2(n1,k), k=1..n1) where S2(n,k) are the Stirling numbers of the second kind.  Sean A. Irvine, May 20 2015
a(n) = n * (A001861(n1) A005493(n2)  A000110(n1)).  Robert Israel, May 21 2015


MAPLE

seq(n*add((2^kk1)*Stirling2(n1, k), k=1..n1), 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^kk1)* StirlingS2[n1, k], {k, 1, n1}]; 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



