%I #15 Jul 03 2023 01:00:25

%S 1,0,2,-6,2,0,2,-1680,10082,0,2,-665280,2,0,3632428802,-36843206400,2,

%T 0,2,-670442572800,3379030566912002,0,2,-71812452903064473600,

%U 1077167364120207360002,0,10002268381116211200002,-3497296636753920000,2,0,2

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

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

%F If p is an odd prime, a(p) = 2.

%t a[n_] := n! * DivisorSum[n, (-1)^(#+1)/(#! * (n/#)!) &]; Array[a, 30] (* _Amiram Eldar_, Jul 03 2023 *)

%o (PARI) a(n) = n!*sumdiv(n, d, (-1)^(d+1)/(d!*(n/d)!));

%Y Cf. A121860, A132962, A363736.

%K sign

%O 1,3

%A _Seiichi Manyama_, Jun 18 2023