A057668 Number of minimal 7-covers of a labeled n-set.

1, 988, 549102, 226064280, 76785889587, 22762819040676, 6092115565691584, 1505097773271664000, 348617485585838373333, 76564317282173987801964, 16080209472530744351164146, 3250906483045575317042337960, 635954979082842132795003641239

Offset: 7

Author

Vladeta Jovovic, Oct 16 2000

Keywords

• easy
• nonn

Links

• Eric Weisstein's World of Mathematics, Minimal cover

Crossrefs

Cf. A000392, A003468, A016111, A046166-A046169, A005783-A005786, A055066 (unlabeled case).

Formula

a(n) = (1/7!) * (127^n - 7 * 126^n + 21 * 125^n - 35 * 124^n + 35 * 123^n - 21 * 122^n + 7 * 121^n - 120^n).

G.f.: x^7 / ((120*x-1)*(121*x-1)*(122*x-1)*(123*x-1)*(124*x-1)*(125*x-1)*(126*x-1)*(127*x-1)). - Colin Barker, Jul 11 2013

Extensions

Additional term from Colin Barker, Jul 11 2013