A132958 - OEIS

%I #10 Sep 29 2017 02:49:34

%S 1,1,7,11,121,479,5041,18479,423361,1844639,39916801,298710719,

%T 6227020801,43606442879,1536517382401,9589093113599,355687428096001,

%U 4259374594675199,121645100408832001,1135353600039859199

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

%H G. C. Greubel, <a href="/A132958/b132958.txt">Table of n, a(n) for n = 1..445</a>

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

%t f[n_] := Block[{d = Divisors@n}, Plus @@ (n!*(-1)^(d + 1)/d!)]; Array[f, 19] (* or *) (* _Robert G. Wilson v_, Sep 13 2007 *)

%t 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 *)

%t Rest[ Range[0, 20]! CoefficientList[ Series[ Sum[1 - Exp[ -x^k], {k, 25}], {x, 0, 20}], x]] (* _Robert G. Wilson v_, Sep 13 2007 *)

%o (PARI) a(n) = n!*sumdiv(n, d, (-1)^(d+1)/d!); \\ _Michel Marcus_, Sep 29 2017

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

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Sep 06 2007

%E More terms from _Robert G. Wilson v_, Sep 13 2007