A132958 a(n) = n!*Sum_{d|n} (-1)^(d+1)/d!.

1, 1, 7, 11, 121, 479, 5041, 18479, 423361, 1844639, 39916801, 298710719, 6227020801, 43606442879, 1536517382401, 9589093113599, 355687428096001, 4259374594675199, 121645100408832001, 1135353600039859199

Offset: 1

Author

Vladeta Jovovic, Sep 06 2007

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..445

Crossrefs

Cf. A057625, A132959, A132960, A132961, A132962, A132963.

Programs

Mathematica

f[n_] := Block[{d = Divisors@n}, Plus @@ (n!*(-1)^(d + 1)/d!)]; Array[f, 19] (* or *) (* Robert G. Wilson v, Sep 13 2007 *)
Rest[ Range[0, 20]! CoefficientList[ Series[ Sum[(-x)^k/(k!*(x^k - 1)), {k, 25}], {x, 0, 20}], x]] (* or *) (* Robert G. Wilson v, Sep 13 2007 *)
Rest[ Range[0, 20]! CoefficientList[ Series[ Sum[1 - Exp[ -x^k], {k, 25}], {x, 0, 20}], x]] (* Robert G. Wilson v, Sep 13 2007 *)

PARI

a(n) = n!*sumdiv(n, d, (-1)^(d+1)/d!); \\ Michel Marcus, Sep 29 2017

Formula

E.g.f.: Sum_{k>0} (-x)^k/(k!*(x^k-1)) or Sum_{k>0}(1-exp(-x^k)).

Extensions

More terms from Robert G. Wilson v, Sep 13 2007