A049056 Number of minimal ordered covers of a labeled n-set.

1, 1, 3, 19, 207, 3691, 103263, 4415419, 283796607, 27094905451, 3813398797023, 786844659227419, 237151202183603007, 104128385332221915211, 66478899089080159079583, 61624041121329496987905019

Offset: 0

Author

N. J. A. Sloane, Michael Somos

Keywords

• nonn
• easy
• nice

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.

Crossrefs

Row sums of A049055.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[ (-1)^i*Binomial[k, i]*(2^k-1-i)^n, {k, 0, n}, {i, 0, k} ]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jan 27 2012, after Michael Somos *)

PARI

{a(n)=sum(k=0, n, sum(i=0, k, (-1)^i*binomial(k, i)*(2^k-1-i)^n))} /* Michael Somos, Oct 16 2006 */

Formula

E.g.f.: Sum_{n>=0} (exp(x)-1)^n*exp(x*(2^n-n-1)), cf. A046165. - Vladeta Jovovic, Sep 01 2005