A132962 - OEIS

%I #10 Sep 29 2017 02:49:27

%S 1,0,2,-3,2,5,2,-140,282,819,2,-20482,2,133419,1527528,-4661085,2,

%T -153296429,2,1402482796,36278688162,13748957859,2,-14081800718427,

%U 5194672859378,7905848380325,2977584150505252,12956452725792600,2,-1314647260913859151

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

%H G. C. Greubel, <a href="/A132962/b132962.txt">Table of n, a(n) for n = 1..500</a>

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

%t Rest[ Range[0, 30]! CoefficientList[ Series[ Sum[1 - Exp[ -x^k/k! ], {k, 30}], {x, 0, 30}], x]] (* _Robert G. Wilson v_, Sep 13 2007 *)

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

%Y Cf. A038041, A132958, A132959, A132960, A132961, A132963.

%K easy,sign

%O 1,3

%A _Vladeta Jovovic_, Sep 06 2007

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