A363736 - OEIS

%I #17 Jul 03 2023 00:53:22

%S 1,0,3,-1,25,59,721,-841,60481,15119,3628801,12972959,479001601,

%T 8648639,134399865601,-218205187201,20922789888001,174888473759999,

%U 6402373705728001,-15205972772390401,3652732042831872001,14079294028799,1124000727777607680001

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

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

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

%F If p is an odd prime, a(p) = 1 + (p-1)!.

%t a[n_] := (n-1)! * DivisorSum[n, (-1)^(#+1)/(#-1)! &]; Array[a, 25] (* _Amiram Eldar_, Jul 03 2023 *)

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

%Y Cf. A087906, A132960, A352013, A363737.

%K sign

%O 1,3

%A _Seiichi Manyama_, Jun 18 2023