A327587 - OEIS

%I #7 Sep 19 2019 02:20:55

%S 1,1,7,29,121,649,5041,42909,364561,3515651,39916801,486821873,

%T 6227020801,86497214231,1307843292757,21004582611869,355687428096001,

%U 6390006277567483,121645100408832001,2435277595236694779,51091124681475552961,1123451899297248225431

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

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

%F a(p) = p! + 1, where p is odd prime.

%t a[n_] := n! Sum[(-1)^(n - d)/(n/d)!^d, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]

%t nmax = 22; CoefficientList[Series[Sum[-(-x)^k/(k! + (-x)^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%o (PARI) a(n) = n!*sumdiv(n, d, (-1)^(n-d)/(n/d)!^d); \\ _Michel Marcus_, Sep 19 2019

%Y Cf. A061095, A327243.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Sep 17 2019